@article{ASENS_1985_4_18_4_563_0, author = {Wang, McKenzie Y. and Ziller, Wolfgang}, title = {On normal homogeneous {Einstein} manifolds}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {563--633}, publisher = {Elsevier}, volume = {Ser. 4, 18}, number = {4}, year = {1985}, doi = {10.24033/asens.1497}, mrnumber = {87k:53113}, zbl = {0598.53049}, language = {en}, url = {https://www.numdam.org/articles/10.24033/asens.1497/} }
TY - JOUR AU - Wang, McKenzie Y. AU - Ziller, Wolfgang TI - On normal homogeneous Einstein manifolds JO - Annales scientifiques de l'École Normale Supérieure PY - 1985 SP - 563 EP - 633 VL - 18 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.24033/asens.1497/ DO - 10.24033/asens.1497 LA - en ID - ASENS_1985_4_18_4_563_0 ER -
%0 Journal Article %A Wang, McKenzie Y. %A Ziller, Wolfgang %T On normal homogeneous Einstein manifolds %J Annales scientifiques de l'École Normale Supérieure %D 1985 %P 563-633 %V 18 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.24033/asens.1497/ %R 10.24033/asens.1497 %G en %F ASENS_1985_4_18_4_563_0
Wang, McKenzie Y.; Ziller, Wolfgang. On normal homogeneous Einstein manifolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 18 (1985) no. 4, pp. 563-633. doi : 10.24033/asens.1497. https://www.numdam.org/articles/10.24033/asens.1497/
[1] Köhlerian Coset Spaces of Semi-simple Lie groups (Proc. Nat. Acad. Sci., U.S.A., Vol. 40, 1954, pp. 1147-1151). | MR | Zbl
,[2] Einstein Manifolds (to appear in "Ergebnisse der Mathematik", Spinger Verlag). | MR | Zbl
,[3] Les variétés riemanniennes homogènes normales simplement connexes à courbure strictement positive (Ann. Sci. Norm. Sup. Pisa, Vol. 15, 1961, pp. 179-246). | Numdam | MR | Zbl
,[4] Curvature Operators : Pinching Estimates and Geometric Examples (Ann. scient. Éc. Norm. Sup., Vol. 11, 1978, pp. 71-92). | Numdam | MR | Zbl
and ,[5] Les sous-groupes fermés de rang maximum des groupes de Lie clos (Comm. Math. Helv., Vol. 23, 1949, pp. 200-221). | MR | Zbl
and , and , Number Theory, Academic Press, N.Y., 1966. |[7] Naturally Reductive Metrics and Einstein Metrics on Compact Lie Groups (Memoirs of the Am. Math. Soc., Vol. 18, No. 215, 1979). | MR | Zbl
and ,[8] Semi-simple Subalgebras of Semi-simple Lie Algebras (Transl. Am. Math. Soc., Series 2, Vol. 6, 1957, pp. 111-244). | Zbl
,[9] Maximal Subalgebras of the Classical Groups (Transl. Am. Math. Soc., Series 2, Vol. 6, 1957, pp. 245-378). | MR | Zbl
,[10] Die Krümmung des Raumes Sp (2)/SU (2) von Berger (Math. Ann., Vol. 164, 1966, pp. 317-323). | MR | Zbl
,[11] Naturally Reductive Metrics of Non-positive Ricci Curvature (Proc. Am. Math. Soc.), Vol. 91, 1984, pp. 287-290. | MR | Zbl
and ,[12] Einstein Metrics on Principal Fibre Bundles (J. Diff. Geom., Vol. 8, 1973, pp. 599-614). | MR | Zbl
,[13] On Differential Geometry and Homogeneous Spaces, I and II (Proc. Nat. Acad. Sc., U.S.A., Vol. 42, 1956, pp. 258-261 and 354-357). | MR | Zbl
,[14] The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group (Amer. J. Math., Vol. 81, 1959, pp. 973-1032). | MR | Zbl
,[15] Foundations of Differential Geometry, Vol. II, Interscience, N.Y., 1969. | Zbl
and ,[16] Einstein Metrics on Fibred Riemannian Structures (Kodai Math. J., Vol. 6, 1983, pp. 340-345). | MR | Zbl
,[17] Remarks on Köhler-Einstein Manifolds (Nagoya Math. J., Vol. 46, 1972, pp. 161-173). | MR | Zbl
,[18] Inclusion Relations Among Transitive Compact Transformation Groups (Transl. Amer. Math. Soc., Series 2, Vol. 50, 1966, pp. 5-58). | Zbl
,[19] On Transitive Compact Transformation Groups (Transl. Amer. Math. Soc., Series 2, Vol. 55, 1966, pp. 153-194).
,[20] Some Homogeneous Einstein Manifolds (Nagoya Math. J., Vol. 39, 1970, pp. 81-106). | MR | Zbl
,[21] Some Examples of Homogeneous Einstein Manifolds in Dimension Seven (Duke Math. J., Vol. 49, 1982, pp. 23-28). | MR | Zbl
,[22] On the Isotropy Representation of a Symmetric Space (to appear in Rend. Sem. Mat. Univers. Politecn. Torino). | MR | Zbl
and ,[23] Isotropy Irreducible Spaces, Symmetric Spaces, and Maximal Subgroups of Classical Groups (in preparation).
and ,[24] Existence and Non-existence of Homogeneous Einstein Metrics, (to appear in Invent. Math.). | MR | Zbl
and ,[25] The Geometry and Structure of Isotropy Irreducible Homogeneous Spaces (Acta Mathematica, Vol. 120, 1968, pp. 59-148) ; Correction (Acta Mathematica, Vol. 152, 1984, pp. 141-142). | MR | Zbl
,[26] Spaces of Constant Curvature, 4th Edition, Publish or Perish Inc., 1977.
,[27] Homogeneous Einstein Metrics on Spheres and Projective Spaces (Math. Ann., Vol. 259, 1982, pp. 351-358). | MR | Zbl
,[28] Homogeneous Einstein Metrics (Global Riemannian Geometry, T.J. WILLMORE and N. HITCHIN Eds., John-Wiley, 1984, pp. 126-135). | MR | Zbl
,- Einstein metrics on aligned homogeneous spaces with two factors, Journal of the London Mathematical Society, Volume 111 (2025) no. 3 | DOI:10.1112/jlms.70120
- Correction: The geometry of compact homogeneous spaces with two isotropy summands, Annals of Global Analysis and Geometry, Volume 66 (2024) no. 2 | DOI:10.1007/s10455-024-09966-9
- The classical and quantum particle on a flag manifold, Classical and Quantum Gravity, Volume 41 (2024) no. 20, p. 205009 | DOI:10.1088/1361-6382/ad7189
- The Lichnerowicz Laplacian on normal homogeneous spaces, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2024 (2024) no. 814, p. 91 | DOI:10.1515/crelle-2024-0038
- Foliated Hopf hypersurfaces in complex hyperbolic quadrics, Annali di Matematica Pura ed Applicata (1923 -), Volume 202 (2023) no. 2, p. 619 | DOI:10.1007/s10231-022-01254-2
- Homogeneous Einstein metrics and butterflies, Annals of Global Analysis and Geometry, Volume 63 (2023) no. 4 | DOI:10.1007/s10455-023-09905-0
- Stability of standard Einstein metrics on homogeneous spaces of non-simple Lie groups, Collectanea Mathematica (2023) | DOI:10.1007/s13348-023-00431-7
- Quantum Flag Manifold
-Models and Hermitian Ricci Flow, Communications in Mathematical Physics, Volume 401 (2023) no. 1, p. 1 | DOI:10.1007/s00220-022-04532-5 - The stability of standard homogeneous Einstein manifolds, Mathematische Zeitschrift, Volume 303 (2023) no. 1, p. 36 (Id/No 16) | DOI:10.1007/s00209-022-03174-6 | Zbl:1510.53059
- Bismut Ricci flat generalized metrics on compact homogeneous spaces, Transactions of the American Mathematical Society (2023) | DOI:10.1090/tran/9013
- Homogeneous Einstein metrics and local maxima of the Hilbert action, Journal of Geometry and Physics, Volume 178 (2022), p. 104544 | DOI:10.1016/j.geomphys.2022.104544
- ISOMETRY GROUPS OF GENERALIZED STIEFEL MANIFOLDS, Transformation Groups, Volume 27 (2022) no. 4, p. 1533 | DOI:10.1007/s00031-022-09778-w
- Non-naturally reductive Einstein metrics on normal homogeneous Einstein manifolds, Communications in Contemporary Mathematics, Volume 23 (2021) no. 08 | DOI:10.1142/s0219199720500790
- New pseudo Einstein metrics on Einstein solvmanifolds, manuscripta mathematica, Volume 166 (2021) no. 3-4, p. 427 | DOI:10.1007/s00229-020-01249-4
- Homogeneous Einstein manifolds based on symplectic triple systems, Communications in Mathematics, Volume 28 (2020) no. 2, p. 139 | DOI:10.2478/cm-2020-0016
- On the volume of orbifold quotients of symmetric spaces, Differential Geometry and its Applications, Volume 71 (2020), p. 101639 | DOI:10.1016/j.difgeo.2020.101639
- Pseudo-Riemannian Einstein metrics on noncompact homogeneous spaces, Journal of Geometry, Volume 111 (2020) no. 1 | DOI:10.1007/s00022-019-0518-7
- On locally homogeneous pseudo-Riemannian compact Einstein manifolds, Journal of Geometry and Physics, Volume 155 (2020), p. 103778 | DOI:10.1016/j.geomphys.2020.103778
- Classification of invariant Einstein metrics on certain compact homogeneous spaces, Science China Mathematics, Volume 63 (2020) no. 4, p. 755 | DOI:10.1007/s11425-018-9357-1
- Structure theory of naturally reductive spaces, Differential Geometry and its Applications, Volume 64 (2019), p. 174 | DOI:10.1016/j.difgeo.2019.02.010
- The isotropy representation of a real flag manifold: Split real forms, Indagationes Mathematicae, Volume 26 (2015) no. 3, p. 547 | DOI:10.1016/j.indag.2015.03.002
- Homogeneous Einstein–Randers metrics on Aloff–Wallach spaces, Journal of Geometry and Physics, Volume 98 (2015), p. 196 | DOI:10.1016/j.geomphys.2015.08.009
- Low Cohomogeneity Actions and Positive Curvature, Lie Groups and Geometric Aspects of Isometric Actions (2015), p. 139 | DOI:10.1007/978-3-319-16613-1_6
- COMPACT HOMOGENEOUS SPACES WITH POSITIVE EULER CHARACTERISTIC AND THEIR 'STRANGE FORMULAE', The Quarterly Journal of Mathematics, Volume 66 (2015) no. 2, p. 507 | DOI:10.1093/qmath/hav009
- The classification of homogeneous Einstein metrics on flag manifolds withb2(M)=1, Bulletin des Sciences Mathématiques, Volume 138 (2014) no. 6, p. 665 | DOI:10.1016/j.bulsci.2013.11.002
- Conformal holonomy, symmetric spaces, and skew symmetric torsion, Differential Geometry and its Applications, Volume 33 (2014), p. 4 | DOI:10.1016/j.difgeo.2013.10.012
- On the characteristic connection of gwistor space, Open Mathematics, Volume 11 (2013) no. 1 | DOI:10.2478/s11533-012-0082-y
- Homogeneous Einstein metrics on 𝐺₂/𝑇, Proceedings of the American Mathematical Society, Volume 141 (2013) no. 7, p. 2485 | DOI:10.1090/s0002-9939-2013-11682-5
- Cohomogeneity one manifolds with a small family of invariant metrics, Geometriae Dedicata, Volume 157 (2012) no. 1, p. 41 | DOI:10.1007/s10711-011-9600-5
- Introduction to Finsler Geometry, Homogeneous Finsler Spaces (2012), p. 1 | DOI:10.1007/978-1-4614-4244-8_1
- Symmetric Finsler Spaces, Homogeneous Finsler Spaces (2012), p. 105 | DOI:10.1007/978-1-4614-4244-8_5
- Weakly Symmetric Finsler Spaces, Homogeneous Finsler Spaces (2012), p. 135 | DOI:10.1007/978-1-4614-4244-8_6
- Homogeneous Randers Spaces, Homogeneous Finsler Spaces (2012), p. 173 | DOI:10.1007/978-1-4614-4244-8_7
- Lie Groups and Homogeneous Spaces, Homogeneous Finsler Spaces (2012), p. 31 | DOI:10.1007/978-1-4614-4244-8_2
- The Group of Isometries, Homogeneous Finsler Spaces (2012), p. 59 | DOI:10.1007/978-1-4614-4244-8_3
- Homogeneous Finsler Spaces, Homogeneous Finsler Spaces (2012), p. 79 | DOI:10.1007/978-1-4614-4244-8_4
- The skew-torsion holonomy theorem and naturally reductive spaces, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012 (2012) no. 664 | DOI:10.1515/crelle.2011.100
- Left-Invariant Pseudo-Einstein Metrics on Lie Groups, Journal of Nonlinear Mathematical Physics, Volume 19 (2012) no. 2, p. 236 | DOI:10.1142/s1402925112500155
- Invariant Hermitian structures and variational aspects of a family of holomorphic curves on flag manifolds, Annals of Global Analysis and Geometry, Volume 40 (2011) no. 1, p. 105 | DOI:10.1007/s10455-011-9248-2
- Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics, Journal of Fixed Point Theory and Applications, Volume 10 (2011) no. 2, p. 307 | DOI:10.1007/s11784-011-0064-x
- INVARIANT EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH TWO ISOTROPY SUMMANDS, Journal of the Australian Mathematical Society, Volume 90 (2011) no. 2, p. 237 | DOI:10.1017/s1446788711001303
- Invariant Einstein metrics on flag manifolds with four isotropy summands, Annals of Global Analysis and Geometry, Volume 37 (2010) no. 2, p. 185 | DOI:10.1007/s10455-009-9183-7
- Integrability of invariant geodesic flows on n-symmetric spaces, Annals of Global Analysis and Geometry, Volume 38 (2010) no. 3, p. 305 | DOI:10.1007/s10455-010-9216-2
- Spectral isolation of naturally reductive metrics on simple Lie groups, Mathematische Zeitschrift, Volume 266 (2010) no. 4, p. 979 | DOI:10.1007/s00209-009-0640-6
- Einstein-RÄume, Differentialgeometrie (2008), p. 219 | DOI:10.1007/978-3-8348-9453-3_8
- Spaces of Riemannian metrics, Journal of Mathematical Sciences, Volume 142 (2007) no. 5, p. 2436 | DOI:10.1007/s10958-007-0185-3
- Geometry of homogeneous Riemannian manifolds, Journal of Mathematical Sciences, Volume 146 (2007) no. 6, p. 6313 | DOI:10.1007/s10958-007-0472-z
- A Class of Homogeneous Einstein Manifolds*, Chinese Annals of Mathematics, Series B, Volume 27 (2006) no. 4, p. 411 | DOI:10.1007/s11401-005-0032-0
- Einstein—Räume, Differentialgeometrie (2005), p. 217 | DOI:10.1007/978-3-322-93422-2_8
- Series of Lie groups, Michigan Mathematical Journal, Volume 52 (2004) no. 2 | DOI:10.1307/mmj/1091112085
- Isometry groups of homogeneous spaces with positive sectional curvature, Differential Geometry and its Applications, Volume 14 (2001) no. 1, p. 57 | DOI:10.1016/s0926-2245(00)00038-3
- Symmetric weights and
-representations, Kodai Mathematical Journal, Volume 23 (2000) no. 2 | DOI:10.2996/kmj/1138044216 - Einstein—Räume, Differentialgeometrie (1999), p. 200 | DOI:10.1007/978-3-322-93981-4_8
- NEW STABLE NORMAL HOMOGENEOUS RIEMANNIAN MANIFOLDS, Kyushu Journal of Mathematics, Volume 53 (1999) no. 2, p. 407 | DOI:10.2206/kyushujm.53.407
- Einstein normal homogeneous Riemannian manifold, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Volume 72 (1996) no. 8 | DOI:10.3792/pjaa.72.197
- Structure of standard homogeneous Einstein manifolds with simple isotropy group. I, Siberian Mathematical Journal, Volume 37 (1996) no. 1, p. 151 | DOI:10.1007/bf02104766
- Structure of standard homogeneous Einstein manifolds with simple isotropy group. II, Siberian Mathematical Journal, Volume 37 (1996) no. 3, p. 542 | DOI:10.1007/bf02104858
- Weakly Symmetric Spaces, Topics in Geometry (1996), p. 355 | DOI:10.1007/978-1-4612-2432-7_15
- Determining summands in tensor products of Lie algebra representations, Journal of Pure and Applied Algebra, Volume 93 (1994) no. 2, p. 135 | DOI:10.1016/0022-4049(94)90108-2
- New invariant Einstein metrics on generalized flag manifolds, Transactions of the American Mathematical Society, Volume 337 (1993) no. 2, p. 981 | DOI:10.1090/s0002-9947-1993-1097162-3
- Einstein metrics and quaternionic Kähler manifolds, Mathematische Zeitschrift, Volume 210 (1992) no. 1, p. 305 | DOI:10.1007/bf02571800
- Einstein metrics on even-dimensional homogeneous spaces admitting a homogeneous Riemannian metric of positive sectional curvature, Siberian Mathematical Journal, Volume 32 (1992) no. 3, p. 455 | DOI:10.1007/bf00970483
- Simply connected compact standard homogeneous Einstein manifolds, Siberian Mathematical Journal, Volume 33 (1992) no. 4, p. 641 | DOI:10.1007/bf00971129
- Compact standard periodic einstein manifolds, Siberian Mathematical Journal, Volume 33 (1992) no. 5, p. 862 | DOI:10.1007/bf00970995
- On isotropy irreducible Riemannian manifolds, Acta Mathematica, Volume 166 (1991) no. 0, p. 223 | DOI:10.1007/bf02398887
- Compact periodic standard Einstein manifolds, Soviet Mathematics. Doklady, Volume 43 (1991) no. 1, pp. 198-201 | Zbl:0810.53035
- Einstein metrics on principal torus bundles, Journal of Differential Geometry, Volume 31 (1990) no. 1 | DOI:10.4310/jdg/1214444095
- Homogeneous Einstein Metrics On Certain Kähler C-Spaces, Recent Topics in Differential and Analytic Geometry (1990), p. 303 | DOI:10.1016/b978-0-12-001018-9.50013-0
- On the twistor space of the six-sphere, Bulletin of the Australian Mathematical Society, Volume 39 (1989) no. 1, p. 119 | DOI:10.1017/s0004972700028021
-
-dimensional contact manifolds with second Betti number , Tohoku Mathematical Journal, Volume 41 (1989) no. 1 | DOI:10.2748/tmj/1178227872 - Coset spaces and ten-dimensional unified theories, Classical and Quantum Gravity, Volume 5 (1988) no. 1, p. 27 | DOI:10.1088/0264-9381/5/1/011
- Metric differential geometri, Differential Geometry, Volume 1263 (1987), p. 171 | DOI:10.1007/bfb0078613
Cité par 72 documents. Sources : Crossref, zbMATH