zbMATH — the first resource for mathematics

An obstruction to the existence of Einstein Kaehler metrics. (English) Zbl 0506.53030

53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q99 Complex manifolds
Full Text: DOI EuDML
[1] Aubin, T.: Equations du type Monge-Ampère sur les variétés kählériennes compactes. C.R. Acad. Sci. Paris283, 119-121 (1976) · Zbl 0333.53040
[2] Blanchard, M.A.: Sur les variétés analytiques complexes. Ann. Sci. Ecole Norm. Sup.73, 157-202 (1956) · Zbl 0073.37503
[3] Bott, R.: Homogeneous vector bundles. Ann. of Math.66, 203-248 (1957) · Zbl 0094.35701
[4] Bourguignon, J.P.: Sur la deuxième conjecture de Calabi, Première classe de Chern et courbure de Ricci: preuve de la conjecture de Calabi. Soc. Math. de France, Astérisque58, 135-147 (1978)
[5] Calabi, E.: Extremal Kähler metrics, Seminar on differential geometry. Ann. of Math. Studies, No. 102, pp. 259-290. Princeton Univ. Press, 1982
[6] Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley-Interscience 1978 · Zbl 0408.14001
[7] Hano, J-I.: Examples of projective manifolds not admitting Kähler metric with constant scalar curvature, preprint · Zbl 0541.53049
[8] Hitchin, N.: On the curvature of rational surfaces. Proc. Symp. Pure Math.27, 65-80 (1975) · Zbl 0321.53052
[9] Ishikawa, K., Sakane, Y.: On complex projective bundles over a KählerC-space. Osaka J. Math.16, 121-132 (1979) · Zbl 0409.53036
[10] Kazdan, J.L.: Gaussian and scalar curvature, an update, Seminar on differential geometry. Ann. of Math. Studies, No. 102, pp. 185-191. Princeton Univ. Press 1982
[11] Kazdan, J.L., Warner, F.W.: Curvature functions for compact 2-manifolds. Ann. of Math.99, 14-47 (1974) · Zbl 0273.53034
[12] Kobayashi, S.: Transformation groups in differential geometry. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0246.53031
[13] Lichnerowicz, A.: Sur les transformations analytiques des variétés kählériennes. C.R. Acad. Sci. Paris244, 3011-3014 (1957
[14] Lichnerowicz, A.: Géometrie des groupes de transformations. Paris: Dunod 1958
[15] Matsushima, Y.: Sur la structure du groupe d’homéomorphismes analytiques d’une certaine variété kaehlérienne. Nagoya Math. J.11, 145-150 (1957) · Zbl 0091.34803
[16] Sakane, Y.: On compact Einstein Kähler manifolds with abundant holomorphic transformations, Manifolds and Lie groups, papers in honor of Matsushima. Progress in Math., pp. 337-358. Boston: Birkhäuser 1981
[17] Sakane, Y.: On nonsingular hyperplane sections of a Hermitian symmetric space, preprint · Zbl 0565.53044
[18] Yau, S.-T.: On the curvature of compact Hermitian manifolds. Invent. Math.25, 213-239 (1974) · Zbl 0299.53039
[19] Yau, S.-T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I. Comm. Pure Appl. Math.31, 339-411 (1978) · Zbl 0369.53059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.