La géométrie métrique des variétés riemanniennes (variations sur la formule $a^2 = b^2 + c^2

La géométrie métrique des variétés riemanniennes (variations sur la formule

a^{2} = b^{2} + c^{2} - 2 b c cos α)

Berger, Marcel

Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 9-66.

MR Zbl | 2 citations dans Numdam

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     author = {Berger, Marcel},
     title = {La g\'eom\'etrie m\'etrique des vari\'et\'es riemanniennes (variations sur la formule $a^2 = b^2 + c^2 - 2bc \cos \alpha)$},
     booktitle = {\'Elie Cartan et les math\'ematiques d'aujourd'hui - Lyon, 25-29 juin 1984},
     series = {Ast\'erisque},
     pages = {9--66},
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     number = {S131},
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Berger, Marcel. La géométrie métrique des variétés riemanniennes (variations sur la formule $a^2 = b^2 + c^2 - 2bc \cos \alpha)$, dans Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 9-66. http://www.numdam.org/item/AST_1985__S131__9_0/

Bibliographie
Cité par

[A] Ambrose (W.). - Parallel translation of Riemannian curvature, Ann. of Math., t. 64, 1956, p. 337-363. | DOI | MR | Zbl

[AV] Alexandrov (A. D.). - La géométrie intérieure des surfaces convexes. - Akademie-Verlag, 1955, (existe en russe et en allemand).

[A-P-S] Atiyah (M.), Patodi (V.), Singer (I.). - Spectral asymmetry and Riemannian Geometry I, Math. Proc. Cambridge Philos. Soc., t. 77, 1975, p. 43-69 | DOI | MR | Zbl

Atiyah (M.), Patodi (V.), Singer (I.). - Spectral asymmetry and Riemannian Geometry II, Math. Proc. Cambridge Philos. Soc., t. 78, 1976, p. 405-432 | DOI | MR | Zbl

Atiyah (M.), Patodi (V.), Singer (I.). - Spectral asymmetry and Riemannian Geometry III, Math. Proc. Cambridge Philos. Soc., t. 79, 1976, p. 315-330. | MR | Zbl

[B-E] Ballmann (W.), Eberlein (P.). - (à paraître).

[B-B-E] Ballmann (W.), Brin (M.), Eberlein (P.). - Structure of manifolds of non-positive curvature I, Preprint Univ. of Maryland 1984. | MR

[B-B-S] Ballmann (W.), Brin (M.), Spatzier (R.). - Structure of manifolds of nonpositive curvature II, (à paraître). | DOI | Zbl

[Ba] Banchoff (T.). - Critical points and curvature for embedded polyhedra, J. Diff. Geometry, t. 1, 1967, p. 245-256. | DOI | MR | Zbl

[Bav] Bavard (C.). - Courbure presque négative en dimension 3. Preprint École Polytechnique 1985.

[B-P] Bavard (C.), Pansu (P.). - Sur le volume minimal de $ℝ^{2}$ . Preprint École Polytechnique 1984.

[B1] Berger (M.). - An extension of Rauch's metric comparison theorem and some applications, Illinois J. Math., t. 6, 1962, p. 700-712. | MR | Zbl

[B2] Berger (M.). - Une caractérisation purement métrique des variétés Riemanniennes à courbure constante, dans E.B. Christoffel, Birkhäuser 1981, p. 480-492. | MR | Zbl

[B3] Berger (M.). - H.E. Rauch, Géomètre différentiel, p. 1-14 de Differential Geometry and Complex Analysis, Berlin, Springer Verlag 1985. | MR | Zbl

[Be] Besse (A.). - Manifolds all of whose geodesics are closed. - Berlin, Springer-Verlag, 1978, (Ergebnisse der Math. n°93). | MR | Zbl

[B1] Blumenthal (L.). - Theory and Applications of Distance Geometry. - Chelsa 1970. | MR | Zbl

[B-M] Blumenthal (L.), Menger (K.). - Studies in Geometry. - Freeman 1970. | MR | Zbl

[B-D-S] Bourguignon (J.-P.), Descahmps (A.), Sentenac (P.). - Conjecture de Hopf sur les produits de variétés et quelques variations particulières d'un produit de métriques, Ann. Sci. École Norm. Sup., t. 5, 1972, p. 277-302 | DOI | EuDML | Numdam | MR | Zbl

Bourguignon (J.-P.), Descahmps (A.), Sentenac (P.). - Conjecture de Hopf sur les produits de variétés et quelques variations particulières d'un produit de métriques, Ann. Sci. École Norm. Sup., t. 6, 1973 p. 1-16. | DOI | EuDML | Numdam | MR | Zbl

[B-P] Bourguignon (J.-P.), Polombo (A.). - Intégrands des nombres caractéristiques et courbure : rien ne va plus dès la dimension 6, J. Diff. Geometry, t. 16, 1981, p. 537-550. | DOI | MR | Zbl

[Bü] Von Braunmühl (A.). - Geodätische Linien und ihre Enveloppen auf dreiaxigen Flächen zweiten Grades, Math. Ann., t. XX, 1882, p. 557-586. | DOI | EuDML | JFM | MR

[Br] Brittain (D.). - (à paraître).

[Bh1] Buchner (M.). - Simplicial structure of the real analytic cut-locus, Proc. A.M.S., t. 64, 1977, p. 118-121. | DOI | MR | Zbl

[Bh2] Buchner (M.). - Stability of the cut-locus in $dim \leq 6$ , Inventiones Math., t. 43, 1977, p. 199-231. | EuDML | MR | Zbl

[Bh3] Buchner (M.). - The structure of the cut-locus in $dim \leq 6$ , Compositio Math., t. 37, 1978, p. 103-119. | EuDML | Numdam | MR | Zbl

[B-C] Bishop (R.), Crittenden (R.). - Geometry of Manifolds. - Academic Press, 1964. | MR | Zbl

[B-Z] Burago (Y.), Zalgaller (D.). - Convex sets in Riemannian spaces of nonegative curvature, Russian Math. Surveys, t. 32-3, 1977, p. 1-57. | DOI | Zbl

[Bs1] Busemann (H.). - The Geometry of Geodesics. - Academic Press, 1955. | MR | Zbl

[Bs] Busemann (H.). - Recent synthetic Differtential Geometry. - Berlin, Springer-Verlag, 1970, (Ergebnisse der Math. n°54). | MR | Zbl

[B-G] Buser (P.), Gromoll (D.). - Gromov's examples of almost negatively curved metrics on S3, prépublication Lausanne 1983.

[B-K] Buser (P.), Karcher (H.). - Gromov's almost flat manifolds, in Astéristique n°81, Soc. Math. France 1981. | Numdam | MR | Zbl

[Ca] Calabi (E.). - (non publié).

[C1] Cartan (É.). - Sur une classe remarquable d'espaces de Riemann, Bull. Soc. Math. France, t. 54, 1926, p. 214-264 | DOI | EuDML | JFM | MR

Cartan (É.). - Sur une classe remarquable d'espaces de Riemann, Bull. Soc. Math. France t. 55, 1927 p. 114-134 ou dans Oeuvres complètes. | DOI | EuDML | JFM | MR

[C2] Cartan (É.). - Sur certaines formes riemanniennes remarquables des géométries à groupe fondamental simple, Ann. Sci. Ecole Norm. Sup., t. 44, 1927, p. 345-467. | DOI | EuDML | JFM | Numdam | MR

[C3] Cartan (É.). - La géométrie des espaces de Riemann. - Fascicule IX, Mémorial des Sciences mathématiques, Gauthier-Villars 1925. | EuDML | JFM | Numdam

[C4] Cartan (É.). - Leçons sur la géométrie des espaces de Riemann. - Gauthier-Villars, 1928, seconde édition 1951. | MR | Zbl

[C5] Cartan (É.). - Groupes simples clos et ouverts et géométrie riemannienne, J. Math. Pures Appl., t. 8, 1929, p. 1-33 ou dans Oeuvres complètes. | EuDML | JFM | Numdam

[Ch1] Cheeger (J.). - Finiteness theorems for a certain class of Riemannian manifolds, Amer. J. Math., t. 92, 1970, p. 61-74. | DOI | MR | Zbl

[Ch2] Cheeger (J.). - On the Hodge theory of Riemannian pseudomanifolds, Proc. Sympos. Pure Math., t. 36, A.M.S., 1980, p. 91-145. | DOI | MR | Zbl

[Ch3] Cheeger (J.). - Spectral Geometry of Singular Riemannian Spaces, J. Diff. Geometry, t. 18, 1983, p. 575-657. | DOI | MR | Zbl

[Ch4] Cheeger (J.). - Analytic torsion and the heat equation, Ann. of Math., t. 109, 1979, p. 259-322. | DOI | MR | Zbl

[C-E] Cheeger (J.), Ebin (D.). - Comparison theorems in Riemannian Geometry. American Elsevier, 1975. | MR | Zbl

[C-G] Cheeger (J.), Gromoll (D.). - On the structure of complete manifolds of nonnegative curvature, Ann. of Math., t. 96, 1974, p. 413-443. | DOI | MR | Zbl

[C-M-S] Cheeger (J.), Müller (W.), Schrader (R.). - On the curvature of piecewise flat spaces, Comm. Math. Phys., t. 92, 1984, p. 405-454. | DOI | MR | Zbl

[C-T] Cheeger (J.), Taylor (M.). - On the diffraction of waves by conical singularities, I, II, Comm. Pure Appl. Math., t. 35, 1982, p. 275-331 et p. 487-529 | DOI | MR | Zbl

[Cr] Crittenden (R.). - Minimum and conjugate points in symmetric spaces, Cand. J. Math, t. 14, 1962, p. 320-328. | DOI | MR | Zbl

[Do] Dodziuk (J.). - Finite-difference approach to the Hodge theory of harmonic forms, Amer. J. Math., t. 98, 1976, p. 79-104. | DOI | MR | Zbl

[D-P] Dodziuk (J.), Patodi (V.). - Riemannian structures and triangulations of manifolds, (preprint). | DOI | MR | Zbl

[Du1] Durumeric (O.). - Manifolds with almost equal diameter and injectivity radius, (thèse). - Stony Brook 1982. | MR

[Du2] Durumeric (O.). - A generalization of Berger's almost ¼-pinched manifolds theorem, I, Bull. Amer. Math. Soc., t. 12, 1985, p. 260-264. | DOI | MR | Zbl

[E1] Eschenburg (J.). - New examples of manifolds of strictly positive curvature, Invent. Math., t. 66, 1982, p. 469-480. | DOI | EuDML | MR | Zbl

[E2] Eschenburg (J.). - Freie isometrische Aktionen auf kompakten Lie-Gruppen mit positiv gekrümmten Orbiträumen, (thèse). - Münster 1983. | MR | Zbl

[E-H] Eschenburg (J.), Heintze (E.). - An elementary proof of the Cheeger-Gromoll splitting theorem, Annals of Global Analysis and Geometry, t. 2, 1984, p. 141-151. | DOI | MR | Zbl

[F²-L-R] Feinberg (G.), Friedberg (R.), Lee (T.), Reu (H.). - Preprint 1984, Columbia Univ.

[Fe] Ferus (D.). - Symmetric submanifolds of Euclidean space, Math. Ann., t. 247, 1980, p. 81-93. | DOI | EuDML | MR | Zbl

[F-L] Friedberg (R.), Lee (T.). - Preprint 1984, Columbia Univ.

[Fu] Fukaya (K.). - Finiteness theorems for negatively curved manifolds, (preprint 1983). | MR | Zbl

[Ga] Gabrielov (A.). - Combinatorial formulas for Pontryagin classes and GL-invariant chains, Functional Anal. Applic., t. 12, 1978, p. 1-7. | MR | Zbl

[Gi] Gasqui (J.). - Équivalence projective et équivalence conforme, Ann. Sci. École Norm. Sup., t. 12, 1979, p. 101-134. | DOI | EuDML | Numdam | MR | Zbl

[G-S] Gluck (H.), Singer (D.). - Scattering of geodesics vector fields, Ann. of Math., t. 108 ; 1978, p. 347-372 | DOI | MR | Zbl

Gluck (H.), Singer (D.). - Scattering of geodesics vector fields, Ann. of Math., t. 110, 1979, p. 202-225. | MR | Zbl

[G-K-M] Gromoll (D.), Klingenberg (W.), Meyer (W.). - Riemannsche Geometrie im Grossen, Berlin, Springer-Verlag 1968, (Lecture Notes in Math., 55). | MR | Zbl

[G-M] Gromoll (D.), Meyer (W.). - On complete open manifolds of positive curvature, Ann. of Math., t. 95, 1969, p. 75-90. | DOI | MR | Zbl

[G-W] Gromoll (D.), Wolf (J.). - Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature, Bull. Amer. Math. Soc., t. 77, 1971, p. 545-552. | DOI | MR | Zbl

[G1] Gromov (M.). - Manifolds of negative curvature, J. Diff. Geometry, t. 13, 1978, p. 223-230. | DOI | MR | Zbl

[G2] Gromov (M.). - Conférences au Collège de France sur les variétés à courbure négative, à paraître rédigées par V. Schroeder.

[G3] Gromov (M.). - Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math., t. 56, 1983, p. 213-307. | Numdam | MR | Zbl

[G4] Gromov (M.). - Curvature, diameter and Betti numbers, Comment. Math. Helv., t. 56, 1981, p. 179-195. | DOI | EuDML | MR | Zbl

[G5] Gromov (M.). - Infinite groups as geometric objects, Proceedings of ICM, Warsaw 1983. | Zbl

[G-L-P] Gromov (M.). - Structures métriques pour les variétés riemanniennes, rédigé par J. Lafontaine et P. Pansu, Textes Math. N°1, CEDIC-Nathan 1980. | MR | Zbl

[G-L] Gromov (M.), Lawson (B.). - Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math., t. 58, 1984. | EuDML | Numdam | MR | Zbl

[G-S] Grove (K.), Shiohama (K.). - A generalized sphere theorem, Ann. of Math., t. 106, 1977, p. 202-211. | MR | Zbl

[Ha] Hadamard (J.). - Les surfaces à courbures opposées et leurs lignes géodésiques, J. Math. Pures Appl., t. 4, 1898, p. 27-73. | EuDML | JFM

[He] Hebda (J.). - Conjugate and cut-loci and the Cartan-Ambrose-Hicks theorem, Indiana Univ. Math. J., t. 31, 1982, p. 17-26. | DOI | MR | Zbl

[H-K] Heintze (E.), Karcher (H.). - A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup., t. 11, 1978, p. 451-470. | DOI | EuDML | Numdam | MR | Zbl

[Hk] Hicks (N.). - Connexion preserving spray maps, Ill. J. Math., t. 10, 1966, p. 661-679. | MR | Zbl

[Hks] Hicks (N.). - Notes on Differential Geometry. - Van Nostrand, 1965. | MR | Zbl

[H-R] Hopf (H.), Rinow (W.). - Über den Begriff der vollständigen differentialgeometrischen Flächen, Comment. Math. Helv., t. 3, 1931, p. 209-225. | DOI | EuDML | JFM | MR | Zbl

[Hs] Hsiang (W. Y.). - On the laws of trigonometries of two-point homogeneous spaces, (preprint Berkeley). | MR | Zbl

[Hu] Huang (H.). - Some remarks on the pinching problem, Bull. Inst. Math. Acad. Sinica, t. 9, 1981, p. 389-401. | MR | Zbl

[Ii] Innami (N.). - Convexity in Riemannian manifolds without focal points, dans Advanced Studies in Pure Math., t. 3, 1984, p. 311-332, Kinokuniya Tokyo et North-Holland, 1984. | DOI | MR | Zbl

[J-K] Jost (J.), Karcher (H.). - Geometrische Methoden zur Gewinnung von $A$ -priori-Schranken für harmonische Abbildungen, Manuscripta math., t. 40, 1982, p. 27-77. | DOI | EuDML | MR | Zbl

[Ka] Karcher (H.). - Vorlesungen über Differential Geometrie, cours polycopié Bonn.

[Kt] Katsuda (A.). - Gromov's convergence theorem and its applications, (preprint 1983). | MR | Zbl

[K1] Klingenberg (W.). - Riemannian Geometry, de Gruyter Studies in Math. n°1 1982. | MR | Zbl

[Kw] Komorowski (J.). - Nets on a Riemannian manifold and finite-dimensional approximations of the Laplacian et $A$ minorization of the firstpositive eigenvalue of the scalar Laplacian, (preprints de Inst. Math. Polish Acad. of Sciences, n°83 et 92). | MR | Zbl

[L-Y] Lawson (H.), Yau (S. T.). - Compact manifolds of nonpositive curvature, J. Diff. Geometry, t. 7, 1972, p. 211-228. | DOI | MR | Zbl

[vMt] Van Mangoldt (H.). - Über diejenigen Punkte auf positiv gekrümmten Flächen welche die Eigenschaft haben, dass die von ihnen ausgehenden geodätischen Linien nie aufhören, kürzeste Linien zu sein, Crelle J., t. 91, 1881, p. 23-52. | EuDML | JFM | MR

[Me] Meyer (D.). - Sur les variétés riemanniennes à opérateur de courbure positif, C.R. Acad. Sci. Paris, t. 272, 1971, p. 482-485. | MR | Zbl

[Mi] Milnor (J.). - Morse theory, Ann. of Math. Studies t. 51, Princeton, 1963. | MR | Zbl

[Mw1] Mostow (G.). - Strong rigidity of locally symmetric spaces, Ann. of Math. Studies, t. 78, 1973, p. 1-195. | MR | Zbl

[Mw2] Mostow (G.). - Discrete Subgroups of Lie Groups, Advances in Math, t. 16, 1975, p. 112-123. | DOI | MR | Zbl

[Mü1] Müller (W.). - Analytic torsion and $R$ -torsion of Riemannian manifolds, Advances in Math., t. 28, 1978, p. 233-305. | DOI | MR | Zbl

[Mü2] Müller (W.). - Spectral theory for Riemannian manifolds with cusps and a related trace formula, Akad. Wiss. GDR report, 1982, et preprint I. H. E. S.. | MR | Zbl

[Mh] Munkholm (H.). - Simplices of maximal volume in hyperbolic space, Gromov's norm and Gromov's proof of Mostow's rigidity theorem (following Thurston), Proc. Symp. Algebraic Topology, Siegen 1979. | MR | Zbl

[My1] Myers (S.). - Connection between differential geometry and topology, I, Duke Math. J., t. 1, 1935, p. 376-391 | JFM | MR | Zbl

Myers (S.). - Connection between differential geometry and topology, II, Duke Math. J., t. 2, 1936, p. 95-102. | DOI | JFM | MR | Zbl

[My2] Myers (S.). - Riemannian manifolds with positive mean curvature, Duke Math. J., t. 8, 1941, p. 401-404. | DOI | JFM | MR | Zbl

[Pa] Palais (R.). - On the differentiability of isometries, Proc. A. M. S., t. 8, 1957, p. 805-807. | DOI | MR | Zbl

[Ps] Peters (S.). - Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, (preprint 1983). | MR | Zbl

[Pé] Poincaré (H.). - Sur les lignes géodésiques des surfaces convexes, Trans. Amer. Math. Soc., t. 5, 1905, p. 237-274. | JFM | MR

[Pr] Preissmann (A.). - Quelques propriétés globales des espaces de Riemann, Comment. Math. Helv., t. 15, 1942-1943, p. 175-216. | DOI | EuDML | MR | Zbl

[Rh] Rauch (H.). - A contribution to differential geometry in the large, Ann. of Math., t. 54, 1951, p. 38-55. | DOI | MR | Zbl

[Re] Regge (T.). - General relativity without coordinates, Nuovo Cimento, t. 19, 1961, p. 551-571. | MR

[Ri] Riemann (B.). - Über die Hypothesen, welche der Geometrie zu Grunde liegen, traduite dans SPIVAK, Differential Geometry, vol. II. | JFM | MR

[Rw] Rinow (W.). - Die innere Geometrie der metrischen Räume, Berlin, Springer-Verlag, 1961, (Grundlehren der Math. Wiss., 105). | MR | Zbl

[Ru] Ruh (E.). - Almost flat manifolds, J. Differential Geom., t. 17, 1982, p. 1-14. | DOI | MR | Zbl

[Rd] Rund (H.). - The differential geometry of Finsler spaces, Berlin, Springer-Verlag, 1959, Grundlehren der Math. Wiss., 101). | MR | Zbl

[Si1] Sakai (T.). - On cut-loci in compact Riemannian spaces, Hokkaido Math. J., t. 6, 1977, p. 136-161. | DOI | MR | Zbl

[Si2] Sakai (T.). - On the structure of cut-loci in compact Riemannian spaces, Math. Annalen, t. 235, 1978, p. 129-148. | DOI | EuDML | MR | Zbl

[Si3] Sakai (T.). - Cut-loci of Berger's spheres, Hokkaido Math. J., t. 10, 1980, p. 143-155. | DOI | MR | Zbl

[Si4] Sakai (T.). - Comparison and finiteness theorems in Riemannian Geometry, Advanced Studies in Pure Math., t. 3, 1984, p. 125-181, Kinokuniya Tokyo et North-Holland, 1984. | DOI | MR | Zbl

[Sr] Schroeder (V.). - Finite volume and fundamental groups on manifolds of negative curvature, J. Differential Geometry, t. 20, 1984, p. 175-183. | DOI | MR | Zbl

[Sr1] Schroeder (V.). - Über die Fundamentalgruppe von Räumen nichtpositiver Krümmung mit endlichem Volumen, Schriftenreihe Math. Inst. Münster, 1984. | MR | Zbl

[Sr2] Schroeder (V.). - A splitting theorem for spaces of nonpositive curvature, Inventiones Math., t. 79, 1985, p. 323-328. | DOI | EuDML | MR | Zbl

[Sa] Shiga (K.). - Hadamard manifolds, Geometry of Geodesics and related topics, p. 239-281. - Kinokuniya, Tokyo et North-Holland (Adv. Studies in Pure Math.), 1984. | MR | Zbl

[Sh] Shiohama (K.). - Topology of complete noncompact manifolds, Adv. Studies in Pure Math., t. 3, Kinokuniya, Tokyo et North Holland, 1984. | DOI | MR | Zbl

[Ss] Simons (J.). - On the transitivity of holonomy systems, Annals of Math., t. 76, 1962, p. 213-234. | DOI | MR | Zbl

[S-T] Siu (Y.-T.), Yau (S. T.). - Compactifications of negatively curved complete Kähler manifolds of finite volume, Ann. of Math. Studies, t. 102, 1982, p. 363-380. | MR | Zbl

[S] Sternberg (S.). - Lectures on Differential Geometry. - Prentice-Hall, 1964. | MR | Zbl

[St] Stone (D.). - Geodesics in piecewise linear manifolds, Trans. Amer. Math. Soc., t. 215, 1976, p. 1-44. | DOI | MR | Zbl

[Ta] Takeuchi (M.). - On conjugate loci and cut-loci of compact symmetric spaces I, Tsukuba J. Math., t. 2, 1978, p. 35-68 | DOI | MR | Zbl

Takeuchi (M.). - On conjugate loci and cut-loci of compact symmetric spaces, II, Tsukuba J. Math., t. 3, 1979, p. 1-29. | DOI | MR | Zbl

[To1] Toponogov (V.). - Riemannian spaces with curvature bounded below, Uspehi Math. Nauk, t. 14, 1959, p. 87-135. | MR

[To2] Toponogov (V.). - Riemannian spaces which contain straight lines, Trans. Amer. Math. Soc., t. 37, 1964, p. 287-290. | Zbl

[Vi1] Ville (M.). - On (¼)-pinched $4$ -dimensional Riemannian manifolds of negative curvature, C. R. Acad. Sci., Paris, 1985. | Zbl

[Vi2] Ville (M.). - Sur le volume des variétés riemanniennes pincées, Bull. Soc. Math. France, 1985. | EuDML | Numdam | MR | Zbl

[Wl] Wall (C. T. C.). - Geometric properties of generic differentiable manifolds, Geometry and Topology, Berlin, Springer-Verlag, 1979, (Lecture Notes in Math, 597). | MR | Zbl

[Wa] Wald (A.). - Begründung einer koordinatenlosen Differentialgeometrie der Flächen, Ergebnisse der Math. Kolloq. Wien, t. 7, 1936, p. 24-46. | JFM | Zbl

[W-A] Wallach (N.), Aloff (S.). - An infinite family of distinct $7$ -manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc., t. 81, 1975, p. 93-97. | DOI | MR | Zbl

[Wr] Warner (F.). - The conjugate locus of Riemannian manifold, Amer. J. Math., t. 87, 1965, p. 575-604. | DOI | MR | Zbl

[We] Weinstein (A.). - On the homotopy type of positively pinched manifolds, Arch. Math., t. 18, 1967, p. 523-524. | DOI | MR | Zbl

[W-M-T] Wheeler (J.), Misner (C.), Thorne (K.). - Gravitation. - Freeman 1974. | MR

[W-P] Wu (C. H.), Pati (V.). - (à paraître).

[Y] Yau (S. T.). - Seminar on Differential Geometry, edited by S.T. YAU, Ann. of Math. Studies, t. 102, 1982, p. 669-706. | MR | Zbl