×

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


MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
14J15 Moduli, classification: analytic theory; relations with modular forms
32J15 Compact complex surfaces
PDF BibTeX XML Cite
Full Text: DOI EuDML

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
[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
[5] Bott, R.: Vector fields and characteristic numbers. Mich. Math. J.14, 231-244 (1967) · Zbl 0145.43801
[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
[9] Griffiths, P.: Holomorphic mappings into canonical algebraic varieties. Ann. of Math.93, 439-458 (1971) · Zbl 0214.48601
[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
[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
[18] Kodaira, K.: On Kähler varieties of restricted type. Ann. Math.60, 28-48 (1954) · Zbl 0057.14102
[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
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.