On immersed compact submanifolds of Euclidean space
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- by Marco Rigoli PDF
- Proc. Amer. Math. Soc. 102 (1988), 153-156 Request permission
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
- David Hoffman and Robert Osserman, The area of the generalized Gaussian image and the stability of minimal surfaces in $S^{n}$ and $\textbf {R}^{n}$, Math. Ann. 260 (1982), no. 4, 437–452. MR 670192, DOI 10.1007/BF01457023
Additional Information
- © Copyright 1988 American Mathematical Society
- 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