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Proceedings of the American Mathematical Society

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An integral formula on the scalar curvature of algebraic manifolds

Author: Jih Hsin Cheng
Journal: Proc. Amer. Math. Soc. 81 (1981), 451-454
MSC: Primary 53C55; Secondary 53C40
MathSciNet review: 597661
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Abstract: It is proved in this note that if the scalar curvature of an $ n$-dimensional algebraic complex submanifold is bigger than $ {n^2}$, then it is totally geodesic.

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  • [1] Bang-yen Chen, Characterizations of Einstein Kaehler manifolds and applications, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 61 (1976), no. 6, 592–595 (1977) (English, with Italian summary). MR 0500756
  • [2] Bang-yen Chen and Koichi Ogiue, Some characterizations of complex space forms in terms of Chern classes, Quart. J. Math. Oxford Ser. (2) 26 (1975), no. 104, 459–464. MR 0405303
  • [3] Shoshichi Kobayashi and Takushiro Ochiai, Characterizations of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ. 13 (1973), 31–47. MR 0316745
  • [4] Koichi Ogiue, Differential geometry of Kaehler submanifolds, Advances in Math. 13 (1974), 73–114. MR 0346719
  • [5] Brian Smyth, Differential geometry of complex hypersurfaces, Ann. of Math. (2) 85 (1967), 246–266. MR 0206881
  • [6] Andrew John Sommese, Hyperplane sections of projective surfaces. I. The adjunction mapping, Duke Math. J. 46 (1979), no. 2, 377–401. MR 534057
  • [7] A. Van de Ven, On the 2-connectedness of very ample divisors on a surface, Duke Math. J. 46 (1979), no. 2, 403–407. MR 534058

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Article copyright: © Copyright 1981 American Mathematical Society