zbMATH — the first resource for mathematics

Compact Kähler manifolds of positive bisectional curvature. (English) Zbl 0442.53056

53C55 Global differential geometry of Hermitian and Kählerian manifolds
Full Text: DOI EuDML
[1] Bers, L., Fohn, F., Schechter, M.: Partial Differential Equations. New York: Interscience Publishers 1964 · Zbl 0128.09404
[2] Bishop, R.L., Goldberg, S.I.: On the other second cohomology group of a Kähler manifold of positive curvature. Proc. Amer. Math. Soc.16, 119-122 (1965) · Zbl 0125.39403
[3] Douady, A.: Le problème de modules pour les sous-espaces analytiques compacts d’un espace analytique donné. Ann. Inst. Fourier (Grenoble)16, 1-95 (1966) · Zbl 0146.31103
[4] Eells, J., Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc.10, 1-68 (1978) · Zbl 0401.58003 · doi:10.1112/blms/10.1.1
[5] Eells, J., Sampson, J.H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math.86, 109-160 (1964) · Zbl 0122.40102 · doi:10.2307/2373037
[6] Fischer, G.: Lineare Faserräume und kohärente Modulgarben über komplexen Räumen. Archiv der Math.18, 609-617 (1967) · Zbl 0177.34402 · doi:10.1007/BF01898870
[7] Frankel, T.: Manifolds with positive curvature. Pacific J. Math.11, 165-174 (1961) · Zbl 0107.39002
[8] Fujiki, A.: Closedeness of the Douady spaces of compact Kähler manifolds. Publ. Math. R.I.M.S. Kyoto Univ.14, 1-52 (1978) · Zbl 0409.32016 · doi:10.2977/prims/1195189279
[9] Goldberg, S.I., Kobayashi, S.: Holomorphic bisectional curvature. J. Diff. Geom.1, 225-234 (1967) · Zbl 0169.53202
[10] Griffiths, P.: Hermitian differential geometry, Chern classes, and positive vector bundles. In: Global Analysis, (D.C. Spencer and S. Iyanaga, eds.) pp. 185-251. Princeton Univ. Press 1969 · Zbl 0201.24001
[11] Grothendieck, A.: Sur la classification des fibrés holomorphes sur la sphère de Riemann. Amer. J. Math.79, 121-138 (1957) · Zbl 0079.17001 · doi:10.2307/2372388
[12] 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
[13] Kobayashi, S., Ochiai, T.: Compact homogeneous complex manifolds with positive tangent bundle. In: Differential Geometry, in honor of K. Yano, pp. 233-242, (S. Kobayashi, M. Obata, and T. Takahashi, eds.) pp. 233-242. Tokyo: Kinokuniya 1972 · Zbl 0249.32005
[14] Kobayashi, S., Ochiai, T.: Three-dimensional compact Kähler manifolds with positive holomorphic bisectional curvature. J. Math. Soc. Japan24, 465-480 (1972) · Zbl 0234.53051 · doi:10.2969/jmsj/02430465
[15] Kobayashi, S., Ochiai, T.: Characterizations of complex projective spaces and hyperquadrics. J. Math. Kyoto Univ.13, 31-47 (1973) · Zbl 0261.32013
[16] Lichnerowicz, A.: Applications harmoniques et variétés kählériennes, Symp. Math.3, 341-402 (1970)
[17] Lieberman, D.: Compactness of the Chow scheme: applications to automorphisms and deformations of Kähler manifolds. Séminaire F. Norguet pp. 140-186, 1976
[18] Mabuchi, T.: ?-actions and algebraic threefolds with ample tangent bundle. Nagoya Math. J.69, 33-64 (1978) · Zbl 0352.32022
[19] Meeks, W., Yau, S.-T.: Topology of three dimensional manifolds and the embedding problems in minimal surface theory · Zbl 0458.57007
[20] Mori, S.: Projective manifolds with ample tangent bundles. Ann. of Math.110, 593-606 (1979) · Zbl 0423.14006 · doi:10.2307/1971241
[21] Newlander, A., Nirenberg, L.: Complex-analytic coordinates in almost complex manifolds. Ann. of Math.65, 391-404 (1957) · Zbl 0079.16102 · doi:10.2307/1970051
[22] Sacks, J., Uhlenbeck, K.: The existence of minimal immersion of 2-spheres · Zbl 0462.58014
[23] Schoen, R., Yau, S.-T.: On univalent harmonic maps between surfaces. Invent. Math44, 265-278 (1978) · Zbl 0388.58005 · doi:10.1007/BF01403164
[24] Siu, Y.-T.: The complex-analyticity of harmonicc maps and the strong rigidity of compact Kähler manifolds. Ann. of Math. in press (1980)
[25] Toledo, D.: On the Schwarz lemma for harmonic maps and characteristic numbers of flat bundles
[26] Wood, J.C.: Holomorphicity of certain harmonic maps from a surface to complex projectiven-space · Zbl 0407.58026
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.