Positively curved complex submanifolds immersed in a complex space form
HTML articles powered by AMS MathViewer
- by Takehiro Itoh PDF
- Proc. Amer. Math. Soc. 72 (1978), 341-345 Request permission
Abstract:
The author gives the partial solution for the conjecture; a Kaehler submanifold in a complex space form of constant holomorphic sectional curvature 1 is totally geodesic if ever its holomorphic sectional curvature is greater than $\frac {1}{2}$.References
- S. S. Chern, M. do Carmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 59–75. MR 0273546
- Takehiro Itoh, Addendum to: “On Veronese manifolds” (J. Math. Soc. Japan 27 (1975), no. 3, 497–506), J. Math. Soc. Japan 30 (1978), no. 1, 73–74. MR 514805, DOI 10.2969/jmsj/03010073
- Koichi Ogiue, Differential geometry of Kaehler submanifolds, Advances in Math. 13 (1974), 73–114. MR 346719, DOI 10.1016/0001-8708(74)90066-8
- S. B. Myers, Riemannian manifolds with positive mean curvature, Duke Math. J. 8 (1941), 401–404. MR 4518
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 341-345
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507335-0
- MathSciNet review: 507335