Submanifolds and a pinching problem on the second fundamental tensors
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- by Masafumi Okumura PDF
- Trans. Amer. Math. Soc. 178 (1973), 285-291 Request permission
Abstract:
This paper gives a sufficient condition for a submanifold of a Riemannian manifold of nonnegative constant curvature to be totally umbilical. The condition will be given by an inequality which is established between the length of the second fundamental tensor and the mean curvature.References
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J. A. Erbacher, Isometric immersions of Riemannian manifolds into space forms, Thesis, Brown University, Providence, R. I., 1970.
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 178 (1973), 285-291
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9947-1973-0317246-1
- MathSciNet review: 0317246