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Koiso, N.

Einstein metrics and complex structures. (English) Zbl 0515.53040

Invent. Math. 73, 71-106 (1983).
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Cited in 4 Reviews
Cited in 51 Documents

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32G05 Deformations of complex structures
58D17 Manifolds of metrics (especially Riemannian)
58H15 Deformations of general structures on manifolds

Keywords:

Einstein metric; complex structures; Kaehler-Einstein structure; Chern class
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Full Text: DOI EuDML

References:

[1] Alexiewicz, A., Orlicz, W.: Analytic operators in real Banach spaces. Studia Math.14, 57-78 (1954) · Zbl 0052.34601
[2] Artin, M.: On the solutions of analytic equations. Invent. math.5, 277-291 (1968) · Zbl 0172.05301 · doi:10.1007/BF01389777
[3] Aubin, T.: Equations du type Monge-Ampère sur les variétés kählériennes compactes. C. R. Acad. Sc. Paris283, 119-121 (1976) · Zbl 0333.53040
[4] Aubin, T.: Equations du type Monge-Ampère sur les variétés kählériennes compactes. Bull. Sc. math.102, 63-95 (1978) · Zbl 0374.53022
[5] Bérard Bergery, L.: Enoncé des théorèmes et mise en équation. Astérisque58, 77-102 (1978)
[6] Berger, M.: Sur quelques variétés d’Einstein compactes. Annali di Math. Pura e Appl.53, 89-96 (1961) · Zbl 0115.39301 · doi:10.1007/BF02417787
[7] Berger, M.: Quelques formules de variation pour une structure riemannienne. Ann. scient. Ec. Norm. Sup. Paris3, 285-294 (1970) · Zbl 0204.54802
[8] Berger, M., Ebin, D.G.: Some decompositions of the space of symmetric tensors on a riemannian manifold. J. Differential Geometry3, 379-392 (1969) · Zbl 0194.53103
[9] Bott, R.: Homogeneous vector bundles. Ann. of Math.66, 203-248 (1957) · Zbl 0094.35701 · doi:10.2307/1969996
[10] Bourguignon, J.-P.: Les surface K3 (Géométrie riemannienne en dimension 4, Exposé No VIII) Séminaire Arthur Besse, CEDIC-NATHAN, Paris 1981, pp. 157-177
[11] Calabi, E., Vessentini, E.: On compact locally symmetric Kähler manifolds. Ann. of Math.71, 472-507 (1960) · Zbl 0100.36002 · doi:10.2307/1969939
[12] DeTurck, D.M., Kazdan, J.L.: Some regularity theorems in riemannian geometry. Ann. Scient. Ec. Norm. Sup. Paris14, 249-260 (1981) · Zbl 0486.53014
[13] Ebin, D.G.: Espace des métriques riemanniennes et mouvement des fluides via les variétés d’applications. Centre de Math. de l’Ecole Polytechnique. Paris 1972 · Zbl 0242.58002
[14] Fu?ik, S., Ne?as, J., Sou?ek, J., Sou?ek, V.: Spectral Analysis of Nonlinear Operators. Lecture Notes in Math., vol. 346. Berlin-Heidelberg-New York: Springer 1973
[15] Fujitani, T.: Compact suitable pinched Einstein manifolds. Bulletin of Faculty of Liberal Arts, Nagasaki Univ. Natural Science19, 1-5 (1979)
[16] Helffer, B.: Rappels sur les espaces fonctionnels utiles aux équations aux dérivées partielles. Astérisque58, 9-22 (1978)
[17] Hirsch, M.W.: Differential topology. GTM 33. New York: Springer 1976
[18] Hitchin, N.: Compact four-dimensional Einstein manifolds. J. Differential Geometry9, 435-441 (1974) · Zbl 0281.53039
[19] Kodaira, K., Nirenberg, L., Spencer, D.C.: On the existence of deformations of complex analytic structures. Ann. of Math.68, 450-459 (1958) · Zbl 0088.38004 · doi:10.2307/1970256
[20] Kodaira, K., Spencer, D.C.: On the variation of almost-complex structure. Algebraic Geometry and Topology (Fox R.H. ed.), Princeton 1957, pp. 139-150. · Zbl 0082.15402
[21] Kodaira, K., Spencer, D.C.: On deformations of complex analytic structures I?II. Ann. of Math.67, 328-466 (1958) · Zbl 0128.16901 · doi:10.2307/1970009
[22] Kodaira, K., Spencer, D.C.: On deformations of complex analytic structures III. Stability theorems for complex structures. Ann of Math.71, 43-76 (1960) · Zbl 0128.16902 · doi:10.2307/1969879
[23] Koiso, N.: Non-deformability of Einstein metrics. Osaka J. Math.15, 419-433 (1978) · Zbl 0392.53030
[24] Koiso, N.: Rigidity and infinitesimal deformability of Einstein metrics. Osaka. J. Math.19, 643-668 (1982) · Zbl 0495.53043
[25] Kuranishi, M.: New proof for the existence of locally complete families of complex structures. Proc. of the Conf. on Complex Analysis in Minneapolis. Berlin-Heidelberg-New York: Springer 1964, pp. 142-154
[26] Lichnerowicz, A.: Géométrie des groupes de transformations. Paris: Dunod 1958
[27] Morrow, J., Kodaira, K.: Complex manifolds. Holt, Rinehart and Winston, Inc., USA 1971 · Zbl 0325.32001
[28] Omori, H.: On the group of diffeomorphisms on a compact manifold. Global Analysis, Proc. Sympos. Pure Math.15, (1968); Amer. Math. Soc pp. 167-183
[29] Palais, R.S.: Foundations of Global non-linear analysis. New York: Benjamin 1968 · Zbl 0164.11102
[30] Tomi, F.: On the finite solvability of Plateau’s Problem. Lectures Notes in Math., vol. 597, 679-695. Berlin-Heidelberg-New York: Springer 1977 · Zbl 0361.53008
[31] Yau, S.T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I. Comm. Pure and Appl. Math.31, 339-411 (1978) · Zbl 0369.53059 · doi:10.1002/cpa.3160310304
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