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On compact Kaehler submanifolds in $ {\bf C}{\rm P}\sp {n+p}$ with nonnegative sectional curvature


Author: Yi Bing Shen
Journal: Proc. Amer. Math. Soc. 123 (1995), 3507-3512
MSC: Primary 53C40; Secondary 53C55
DOI: https://doi.org/10.1090/S0002-9939-1995-1277132-X
MathSciNet review: 1277132
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Abstract: A complete classification for nonnegatively curved compact Kaehler submanifolds $ {M^n}$ in $ \mathbb{C}{P^{n + p}}$ with $ p < n$ is given, so that a conjecture of K. Ogiue is resolved partially.


References [Enhancements On Off] (What's this?)

  • [1] K. Ogiue, Differential geometry of Kaehler submanifolds, Adv. Math. 13 (1974), 73-114. MR 0346719 (49:11444)
  • [2] A. Ros, Positively curved Kaehler submanifolds, Proc. Amer. Math. Soc. 93 (1985), 329-331. MR 770547 (86c:53046)
  • [3] A. Ros and L. Verstraelen, On a conjecture of K. Ogiue, J. Differential Geom. 19 (1984), 561-566. MR 755238 (85i:53062)
  • [4] A. Ros, A characterization of seven compact Kaehler submanifolds by holomorphic pinching, Ann. of Math. (2) 121 (1985), 377-382. MR 786353 (86j:53085)
  • [5] J. H. Cheng, An integral formula on the scalar curvature of algebraic manifolds, Proc. Amer. Math. Soc. 31 (1981), 451-454. MR 597661 (82b:53085)
  • [6] W. M. Sheng, Kaehler hypersurfaces with positive sectional curvature in a complex projective space, Chinese Ann. Math. Ser. B 15 (1994), 69-74. MR 1270756 (95d:53075)
  • [7] C. Z. Ouyang and Z. Q. Li, The locally symmetric Bochner-Kaehler manifolds and their Kaehler submanifolds, Chinese Ann. Math. Ser. A 11 (1990), 547-552. MR 1092043 (92b:53026)
  • [8] H. Nakagawa and R. Takagi, On locally symmetric Kaehler submanifolds in a complex projective space, J. Math. Soc. Japan 28 (1976), 638-667. MR 0417463 (54:5513)
  • [9] M. Takeuchi, Homogeneous Kaehler submanifolds in complex projective spaces, Japan J. Math. 4 (1978), 171-219. MR 528871 (80i:32059)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1277132-X
Keywords: Kaehler submanifold, complex projective space, sectional curvature
Article copyright: © Copyright 1995 American Mathematical Society

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