@book{AST_1979__62__R1_0, author = {Dombrowski, Peter}, title = {150 years after {Gauss'} {\guillemotleft} disquisitiones generales circa superficies curvas {\guillemotright}}, series = {Ast\'erisque}, publisher = {Soci\'et\'e math\'ematique de France}, number = {62}, year = {1979}, zbl = {0406.01007}, mrnumber = {535996}, language = {en}, url = {http://www.numdam.org/item/AST_1979__62__R1_0/} }
Dombrowski, Peter. 150 years after Gauss' « disquisitiones generales circa superficies curvas ». Astérisque, no. 62 (1979), 157 p. http://numdam.org/item/AST_1979__62__R1_0/
[1] Parallel translation of Riemannian curvature, Ann. of Math. 64 (1956), 337-363. | MR | Zbl | DOI
:[2] Differential geometrie, 5th ed., Springer, Berlin 1973.
and :[2'] Les variétés riemanniennes -pincées, Ann. Scuola Norm. Sup. Pisa III, 14 (1960) 161-170. | MR | Zbl | EuDML | Numdam
:Les variétés riemanniennes l/4-pincées, C. R. Acad. Sc. Paris, t. 250 A (1960) 442-444. | MR | Zbl
[3] J. de l'Ecole Polytechnique 19 (1848), 131 ff.
:[4] Leçons sur la géométrie des espaces de Riemann, 2nd ed., Gauthier-Villars, Paris 1951. | MR | Zbl
:[5] On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96 (1972), 413-433. | MR | Zbl | DOI
and :[6] A simple intrisic proof of the Gauβ-Bonnet formula for closed Riemannian manifolds, Ann. of Math. 45 (1944), 747-752. | MR | Zbl | DOI
:[7] Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, Lausanne 1744. | Zbl
:[8] Manifolds with preassigned curvature - a survey, Bull. Amer. Soc. 81 (1975), 313-329. | MR | Zbl | DOI
:[9] Riemannsche Geometrie im Groβen, Lecture Notes in Math. 55, Springer, Berlin 1968. | MR | Zbl
, , :[10] On complete open manifolds of positive curvature, Ann. of Math. 90 (1969), 75-90. | MR | Zbl | DOI
and :[11] Über die Curvatura integra geschlossener Hyperflächen, Math. Ann. 95 (1925), 313-399. | JFM | EuDML | MR
:[12] Proceedings of the International Congress of Mathematicians 1958, Cambridge University Press, 1960. | Zbl
:[13] Demonstratio et amplificatio nova Gaussiani de quadratura integra trianguli in data superficie e lineis brevissimis formati, Crelle Journ. 16 (1837), 344-350. | MR | Zbl | EuDML | DOI
:[14] Anwendungen der Alexandrowschen Winkelvergleichssätze, Manuscripta Math. 2 (1970), 77-102. | MR | Zbl | EuDML | DOI
:[15] Foundations of Differential Geometry, vol. I (1963). | MR | Zbl
and :Foundations of Differential Geometryvol. II (1969), Wiley, New York. | MR | Zbl
and :[16] Nouvelle solution du problème du mouvement de rotation corps de figure quelconque, ouvres de Lagrange, III, 572-616, Gauthier- Vi1lars, Paris.
:[17] Éléments de Géométrie, 12ème éd., Paris, 1823. | EuDML
:Histoire de l'Académie royale des Sciences avec les Mémoires de Mathématique et Physique", Paris 1787, p. 338.
The first publication of theses results can be found in : "[18] Bemerkung über die Abwicklung krummer Linien von Flächen, Crelle J. 6 (1830), 159-161. | MR | EuDML | Zbl | DOI
:[19] The imbedding problem for Riemann manifolds, Ann. of Math. (1956), 20-63. | MR | Zbl | DOI
:[20] Opuscula mathematica, rec. I, Castillioneus, vol. 1, Lausanne und Genf, 1744.
:[21] Gesammelte Mathematische Werke, 2nd ed., Leipzig, Teubner, 1892. | MR
:[22] Die innere Geometrie der metrischen Räume, Springer, Berlin 1961. | MR | Zbl | DOI
:[23] Daten aus dem Leben und Wirken von Carl Friedrich Gauβ, on the occasion of the centenary of C.F. Gauss' death, 23 February, 1955, Teubner, Leipzig 1957, 15-36.
:[24] Gauβ als Geometer, G.W. 10, 2, Abhandlung 4, 1-123.
:[25] Allgemeine Flächentheorie von C.F. Gauβ", German translation (with notes) of the "Disquisitiones generales circa superficies curvas", Ostwalds's Klassiker der Exakten Wissenschaften Nr. 5, 5-te Aufl., Akad. Verlagsgesellschaft m.b.H., Leipzig 1921. | JFM
: "[26] Über die Eigenschaften des Linienelements der Flächen von constantem Krümmungsmaβ, Crelle Journ. 94 (1883), 181-102. | MR | JFM | EuDML
:[27] Spaces of constant curvature, McGraw-Hill, New York 1967. | MR | Zbl
:[28] Differential Geometry and Symmetric Spaces, Academic Press, New York 1962. | MR | Zbl
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