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Isometric immersions of complete Riemannian manifolds into Euclidean space


Authors: Christos Baikousis and Themis Koufogiorgos
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
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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 [Enhancements On Off] (What's this?)

  • [1] H. Jacobowitz, Isometric embedding of a compact Riemannian manifold into euclidean space, Proc. Amer. Math. Soc. 40 (1973), 245-246. MR 0375173 (51:11369)
  • [2] S. Kobayashi and N. Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Appl. Math., no. 15, Interscience, New York, 1969.
  • [3] H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. MR 0215259 (35:6101)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560590-2
Keywords: Isometric immersion, scalar curvature, sectional curvature, complete Riemannian manifold
Article copyright: © Copyright 1980 American Mathematical Society

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