Isometric immersions of complete Riemannian manifolds into Euclidean space
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- by Christos Baikousis and Themis Koufogiorgos PDF
- Proc. Amer. Math. Soc. 79 (1980), 87-88 Request permission
Abstract:
Let M be a complete Riemannian manifold of dimension n, with scalar curvature bounded from below. If the isometric immersion of M into euclidean space of dimension $n + q,q \leqslant n - 1$, is included in a ball of radius $\lambda$, then the sectional curvature K of M satisfies ${\lim \sup _M}K \geqslant {\lambda ^{ - 2}}$. The special case where M is compact is due to Jacobowitz.References
- Howard Jacobowitz, Isometric embedding of a compact Riemannian manifold into Euclidean space, Proc. Amer. Math. Soc. 40 (1973), 245–246. MR 375173, DOI 10.1090/S0002-9939-1973-0375173-3 S. Kobayashi and N. Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Appl. Math., no. 15, Interscience, New York, 1969.
- Hideki Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205–214. MR 215259, DOI 10.2969/jmsj/01920205
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 87-88
- MSC: Primary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1980-0560590-2
- MathSciNet review: 560590