Scalar curvature, inequality and submanifold
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- by Bang-yen Chen and Masafumi Okumura PDF
- Proc. Amer. Math. Soc. 38 (1973), 605-608 Request permission
Abstract:
Using an inequality relation between scalar curvature and length of second fundamental form, we may conclude that a submanifold must have nonnegative (or positive) sectional curvatures. An application to compact submanifolds in obtained.References
- Bang-yen Chen, On the mean curvature of submanifolds of euclidean space, Bull. Amer. Math. Soc. 77 (1971), 741–743. MR 284953, DOI 10.1090/S0002-9904-1971-12792-1
- 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
- Masafumi Okumura, Hypersurfaces and a pinching problem on the second fundamental tensor, Amer. J. Math. 96 (1974), 207–213. MR 353216, DOI 10.2307/2373587 —, Submanifolds and a pinching problem on the second fundamental tensor (to appear).
- Brian Smyth, Submanifolds of constant mean curvature, Math. Ann. 205 (1973), 265–280. MR 334102, DOI 10.1007/BF01362697
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 605-608
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1973-0343217-0
- MathSciNet review: 0343217