Submanifolds in a euclidean hypersphere
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- by Bang-yen Chen
- Proc. Amer. Math. Soc. 27 (1971), 627-628
- DOI: https://doi.org/10.1090/S0002-9939-1971-0270309-5
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Abstract:
Let $M$ be an oriented closed $n$-dimensional submanifold of a euclidean ($(n + N)$-space ${E^{n + N}}$. Let $X$ and $H$ be the position vector field and the mean curvature vector field of $M$ in ${E^{n + N}}$. Then $M$ is contained in a hypersphere of ${E^{n + N}}$ centered at $c$ when and only when either $(X - c) \cdot H \geqq - 1$ or $(X - c)\cdot H \leqq - 1$.References
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 627-628
- MSC: Primary 53.74
- DOI: https://doi.org/10.1090/S0002-9939-1971-0270309-5
- MathSciNet review: 0270309