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Proceedings of the American Mathematical Society

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On immersed compact submanifolds of Euclidean space


Author: Marco Rigoli
Journal: Proc. Amer. Math. Soc. 102 (1988), 153-156
MSC: Primary 53C42,; Secondary 53C21
DOI: https://doi.org/10.1090/S0002-9939-1988-0915735-6
MathSciNet review: 915735
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Abstract: Given an immersion $ f:M \to {{\mathbf{R}}^n}$ of a compact Riemannian manifold $ M$ we prove a simple criterion involving the tension field of $ f$ to determine whether or not $ f$ is an isometry.


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

  • [1] D. Hoffman and R. Osserman, The area of the generalized gaussian image and the stability of minimal surface in $ {S^n}$ and $ {{\mathbf{R}}^n}$, Math. Ann. 260 (1982), 437-452. MR 670192 (84a:53006)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0915735-6
Keywords: Isometric immersion, tension field, ratio of the volume elements
Article copyright: © Copyright 1988 American Mathematical Society

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