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Yau, Shing-Tung

On the curvature of compact Hermitian manifolds. (English) Zbl 0299.53039

Invent. Math. 25, 213-239 (1974).
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Cited in 54 Documents

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
14J15 Moduli, classification: analytic theory; relations with modular forms
32J15 Compact complex surfaces
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\textit{S.-T. Yau}, Invent. Math. 25, 213--239 (1974; Zbl 0299.53039)
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References:

[1] Andreotti, A.: On the complex structures of a class of simply-connected manifolds. In: Algebraic Geometry and Topology; A Symposium in Honor of S. Lefschetz, Princeton University Press, Princeton, N. J., pp. 53-77, 1957 · Zbl 0141.37404
[2] Atiyah, M.F.: Complex fiber bundles and ruled surfaces. Proc. London Math. Soc.5, 407-434 (1955) · Zbl 0174.52804 · doi:10.1112/plms/s3-5.4.407
[3] Aubin, T.: Metriques Riemanniennes et courbure. J. Differential Geometry4, 383-424 (1970) · Zbl 0212.54102
[4] Bloch, S., Gieseker, D.: The positivity of the Chern classes of an ample vector bundle. Inventiones math.12, 112-117 (1971) · Zbl 0212.53502 · doi:10.1007/BF01404655
[5] Bott, R.: Vector fields and characteristic numbers. Mich. Math. J.14, 231-244 (1967) · Zbl 0145.43801 · doi:10.1307/mmj/1028999721
[6] Chern, S.S.: On holomorphic mappings of Hermitian manifolds of the same dimension. In: Proc. Symp. Pure Math. 11, Amer. Math. Soc., Providence, R.I., pp. 157-170, 1968 · Zbl 0184.31202
[7] Frankel, T.: Manifolds with positive curvature. Pacific J. Math.11, 165-174 (1961) · Zbl 0107.39002
[8] Frankel, T.: Fixed points and torsions of Kähler manifolds. Ann. of Math.70, 1-8 (1959) · Zbl 0088.38002 · doi:10.2307/1969889
[9] Griffiths, P.: Holomorphic mappings into canonical algebraic varieties. Ann. of Math.93, 439-458 (1971) · Zbl 0214.48601 · doi:10.2307/1970883
[10] Griffiths, P.: Hermitian differential geometry, Chern classes, and positive vector bundles. In: Global Analysis, Princeton Math. Series29, 185-251 (1969) · Zbl 0201.24001
[11] Hartshorne, R.: Ample subvarieties of algebraic varieties. In: Lecture Notes in Mathematics156, Berlin-Heidelberg-New York: Springer 1970 · Zbl 0208.48901
[12] Hartshorne, R.: Ample vector bundles. Inst. Hautes Études Sci. Publ. Math. 55-94 (1966) · Zbl 0173.49003
[13] Howard, A., Smyth, B.: Kähler surfaces of nonnegative curvature. J. Differential Geometry5, 491-502 (1971) · Zbl 0227.53021
[14] Hirzebruch, F.: Topological Methods in Algebraic Geometry. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0138.42001
[15] Kobayashi, S., Nomizu, K.: Foundations of differential geometry. In: Interscience Tracts I (1963), and II (1968), New York: Wiley
[16] Kobayashi, S., Ochiai, T.: On complex manifolds with positive tangent bundles. J. Math. Soc. Japan22, 499-525 (1970) · Zbl 0197.36003 · doi:10.2969/jmsj/02240499
[17] Kodaira, K.: On the structure of compact complex analytic surfaces, I, II, III, IV. Amer. J. Math.86, 751-798 (1964);88, 687-721 (1966);90, 55-83 (1968);90, 1048-1066 (1968) · Zbl 0137.17501 · doi:10.2307/2373157
[18] Kodaira, K.: On Kähler varieties of restricted type. Ann. Math.60, 28-48 (1954) · Zbl 0057.14102 · doi:10.2307/1969701
[19] Lichnerowicz, A.: Sur les transformations analytiques d’une variete Kähleriene compacte. Colloque Geom. Diff. Global, Bruxelles, pp. 11-26, 1958
[20] Matsushima, Y.: Hodge manifolds with zero first Chern class. J. Differential Geometry3, 477-489 (1969) · Zbl 0201.25902
[21] Matsushima, Y.: Sur les espaces homogenes complexes. Nagoya Math. J.18, 1-12 (1961)
[22] Morrow, J., Kodaira, K.: Complex Manifolds. New York: Holt, Reinhart & Winston 1971 · Zbl 0325.32001
[23] Moore, J.D.: Isometric immersions of Riemannian products. J. Differential Geometry5, 159-168 (1971) · Zbl 0213.23804
[24] Nagano, T.: Homogeneous sphere bundles and the isotropic Riemannian manifolds. Nagoya Math. J.15, 29-55 (1959) · Zbl 0086.36601
[25] Suwa, T.: On ruled surfaces of genus 1. J. Math. Soc. Japan2, 258-291 (1969) · Zbl 0175.47902
[26] Van de Ven, A.: On holomorphic fields of complex line elements with isolated singularities. Ann. Inst. Fourier (Grenoble)14, 99-130 (1964) · Zbl 0136.20702
[27] Wang, H.C.: Closed manifolds with homogeneous complex structure. Amer. J. Math.76, 1-32 (1954) · Zbl 0055.16603 · doi:10.2307/2372397
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