On normal homogeneous Einstein manifolds
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 18 (1985) no. 4, pp. 563-633.
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     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 = {http://archive.numdam.org/articles/10.24033/asens.1497/}
}
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Wang, McKenzie Y.; Ziller, Wolfgang. On normal homogeneous Einstein manifolds. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 18 (1985) no. 4, pp. 563-633. doi : 10.24033/asens.1497. http://archive.numdam.org/articles/10.24033/asens.1497/

[1] A. Borel, Köhlerian Coset Spaces of Semi-simple Lie groups (Proc. Nat. Acad. Sci., U.S.A., Vol. 40, 1954, pp. 1147-1151). | MR | Zbl

[2] A. Besse, Einstein Manifolds (to appear in "Ergebnisse der Mathematik", Spinger Verlag). | MR | Zbl

[3] M. Berger, 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] J. P. Bourguignon and H. Karcher, Curvature Operators : Pinching Estimates and Geometric Examples (Ann. scient. Éc. Norm. Sup., Vol. 11, 1978, pp. 71-92). | Numdam | MR | Zbl

[5] A. Borel and J. De Siebenthal, Les sous-groupes fermés de rang maximum des groupes de Lie clos (Comm. Math. Helv., Vol. 23, 1949, pp. 200-221). | MR | Zbl

[6] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, N.Y., 1966. | MR | Zbl

[7] J. E. D'Atri and W. Ziller, Naturally Reductive Metrics and Einstein Metrics on Compact Lie Groups (Memoirs of the Am. Math. Soc., Vol. 18, No. 215, 1979). | MR | Zbl

[8] E. B. Dynkin, Semi-simple Subalgebras of Semi-simple Lie Algebras (Transl. Am. Math. Soc., Series 2, Vol. 6, 1957, pp. 111-244). | Zbl

[9] E. B. Dynkin, Maximal Subalgebras of the Classical Groups (Transl. Am. Math. Soc., Series 2, Vol. 6, 1957, pp. 245-378). | MR | Zbl

[10] H. Eliasson, Die Krümmung des Raumes Sp (2)/SU (2) von Berger (Math. Ann., Vol. 164, 1966, pp. 317-323). | MR | Zbl

[11] C. Gordon and W. Ziller, Naturally Reductive Metrics of Non-positive Ricci Curvature (Proc. Am. Math. Soc.), Vol. 91, 1984, pp. 287-290. | MR | Zbl

[12] G. Jensen, Einstein Metrics on Principal Fibre Bundles (J. Diff. Geom., Vol. 8, 1973, pp. 599-614). | MR | Zbl

[13] B. Konstant, 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] B. Kostant, 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] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II, Interscience, N.Y., 1969. | Zbl

[16] T. Matsuzawa, Einstein Metrics on Fibred Riemannian Structures (Kodai Math. J., Vol. 6, 1983, pp. 340-345). | MR | Zbl

[17] Y. Matsushima, Remarks on Köhler-Einstein Manifolds (Nagoya Math. J., Vol. 46, 1972, pp. 161-173). | MR | Zbl

[18] A. L. Oniščik, Inclusion Relations Among Transitive Compact Transformation Groups (Transl. Amer. Math. Soc., Series 2, Vol. 50, 1966, pp. 5-58). | Zbl

[19] A. L. Oniščik, On Transitive Compact Transformation Groups (Transl. Amer. Math. Soc., Series 2, Vol. 55, 1966, pp. 153-194).

[20] A. Sagle, Some Homogeneous Einstein Manifolds (Nagoya Math. J., Vol. 39, 1970, pp. 81-106). | MR | Zbl

[21] M. Wang, Some Examples of Homogeneous Einstein Manifolds in Dimension Seven (Duke Math. J., Vol. 49, 1982, pp. 23-28). | MR | Zbl

[22] M. Wang and W. Ziller, On the Isotropy Representation of a Symmetric Space (to appear in Rend. Sem. Mat. Univers. Politecn. Torino). | MR | Zbl

[23] M. Wang and W. Ziller, Isotropy Irreducible Spaces, Symmetric Spaces, and Maximal Subgroups of Classical Groups (in preparation).

[24] M. Wang and W. Ziller, Existence and Non-existence of Homogeneous Einstein Metrics, (to appear in Invent. Math.). | MR | Zbl

[25] J. A. Wolf, 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] J. A. Wolf, Spaces of Constant Curvature, 4th Edition, Publish or Perish Inc., 1977.

[27] W. Ziller, Homogeneous Einstein Metrics on Spheres and Projective Spaces (Math. Ann., Vol. 259, 1982, pp. 351-358). | MR | Zbl

[28] W. Ziller, Homogeneous Einstein Metrics (Global Riemannian Geometry, T.J. WILLMORE and N. HITCHIN Eds., John-Wiley, 1984, pp. 126-135). | MR | Zbl

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