# zbMATH — the first resource for mathematics

Differential geometry of Kaehler submanifolds. (English) Zbl 0275.53035

##### MSC:
 53C55 Global differential geometry of Hermitian and Kählerian manifolds 53C40 Global submanifolds 32M10 Homogeneous complex manifolds
Full Text:
##### References:
 [1] Abe, K, A characterization of totally geodesic submanifolds in SN and CPN by an inequality, Tohoku math. J., 23, 219-244, (1971) · Zbl 0245.53053 [2] Berger, M, Pincement riemannien et pincement holomorphe, Ann. scuola norm. sup. Pisa, 14, 151-159, (1960) · Zbl 0094.34901 [3] Bishop, R.L; Goldberg, S.I, Some implications of the generalized Gauss-Bonnet theorem, Trans. amer. math. soc., 112, 508-535, (1964) · Zbl 0133.15101 [4] Bishop, R.L; Goldberg, S.I, On the topology of positively curved Kaehler manifolds II, Tohoku math. J., 17, 310-318, (1965) · Zbl 0134.17906 [5] Calabi, E, Isometric imbedding of complex manifolds, Ann. of math., 58, 1-23, (1953) · Zbl 0051.13103 [6] Calabi, E, Metric Riemann surfaces, Ann. of math. studies, 77-85, (1953) · Zbl 0053.05103 [7] Chen, B.Y; Ludden, G.D, Riemann surfaces in complex projective spaces, (), 561-566 · Zbl 0231.53062 [8] Chern, S.S, On Einstein hypersurfaces in a Kaehlerian manifold of constant holomorphic sectional curvature, J. differential geometry, 1, 21-31, (1967) · Zbl 0168.19505 [9] Chern, S.S; doCarmo, M.P; Kobayashi, S, Minimal submanifolds of a sphere with second fundamental form of constant length, (), 59-75 · Zbl 0216.44001 [10] Goldberg, S.I; Kobayashi, S, Holomorphic bisectional curvature, J. differential geometry, 1, 225-233, (1967) · Zbl 0169.53202 [11] Hirzebruch, F, Topological methods in algebraic geometry, (1966), Springer · Zbl 0138.42001 [12] Kobayashi, S, Hypersurfaces of complex projective space with constant scalar curvature, J. differential geometry, 1, 369-370, (1967) · Zbl 0157.28501 [13] Kobayashi, S; Nomizu, K, Foundations of differential geometry, II, (1969), Interscience · Zbl 0175.48504 [14] Kobayashi, S; Ochiai, T, On complex manifolds with positive tangent bundles, J. math. soc. Japan, 22, 499-525, (1970) · Zbl 0197.36003 [15] Kobayashi, S; Ochiai, T, Compact homogeneous complex manifolds with positive tangent bundle, (), 221-232, in honor of K. Yano [16] Lawson, H.B, The Riemannian geometry of holomorphic curves, () · Zbl 0217.47006 [17] Myers, S, Riemannian manifolds with positive Mean curvature, Duke math. J., 8, 401-404, (1941) · JFM 67.0673.01 [18] Nomizu, K; Smyth, B, Differential geometry of complex hypersurfaces II, J. math. soc. Japan, 20, 498-527, (1968) · Zbl 0181.50103 [19] Ogiue, K, Complex submanifolds of the complex projective space with second fundamental form of constant length, Kodai math. sem. rep., 21, 252-254, (1969) · Zbl 0175.48501 [20] Ogiue, K, Complex hypersurfaces of a complex projective space, J. differential geometry, 3, 253-256, (1969) · Zbl 0187.19002 [21] Ogiue, K, On compact complex submanifolds of the complex projective space, Tohoku math. J., 22, 95-97, (1970) · Zbl 0191.51902 [22] Ogiue, K, Scalar curvature of complex submanifolds of a complex projective space, J. differential geometry, 5, 229-232, (1971) · Zbl 0211.24301 [23] Ogiue, K, Differential geometry of algebraic manifolds, (), 355-372, in honor of K. Yano [24] Ogiue, K, Positively curved complex hypersurfaces immersed in a complex projective space, Tohoku math. J., 24, 51-54, (1972) · Zbl 0235.53043 [25] Ogiue, K, Positively curved complex submanifolds immersed in a complex projective space, J. differential geometry, 7, 603-606, (1972) · Zbl 0271.53050 [26] Ogiue, K, Positively curved complex submanifolds immersed in a complex projective space II, Hokkaido math. J., 1, 16-20, (1972) · Zbl 0246.53055 [27] Ogiue, K, On Kaehler immersions, Can. J. math., 24, 1178-1182, (1972) · Zbl 0229.53047 [28] Ogiue, K, n-dimensional complex space forms immersed in $$[n + (n(n + 1)2)]- dimensional$$ complex space forms, J. math. soc. Japan, 24, 518-526, (1972) · Zbl 0235.53040 [29] O’Neill, B, Isotropic and Kaehler immersions, Can. J. math., 17, 907-915, (1965) · Zbl 0171.20503 [30] Smyth, B, Differential geometry of complex hypersurfaces, Ann. of math., 85, 246-266, (1967) · Zbl 0168.19601 [31] Smyth, B, Homogeneous complex hypersurfaces, J. math. soc. Japan, 20, 643-647, (1968) · Zbl 0165.24803 [32] {\scS. Tanno}, Compact complex submanifolds immersed in complex projective spaces, to appear. · Zbl 0279.53052 [33] Tanno, S, 2-dimensional complex submanifolds immersed in complex projective spaces, Tohoku math. J., 24, 71-78, (1972) · Zbl 0241.53039 [34] Tsukamoto, Y, On Kaehlerian manifolds with positive holomorphic sectional curvature, (), 333-335 · Zbl 0078.14205 [35] Wirtinger, W, Eine determinantenidentität und ihre anwendung auf analytische gebilde in euclidischer und hermitischer massbestimmung, Monatsh. math. phys., 44, 343-365, (1936) · Zbl 0015.07602
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.