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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Isometric embedding of a compact Riemannian manifold into Euclidean space


Author: Howard Jacobowitz
Journal: Proc. Amer. Math. Soc. 40 (1973), 245-246
MSC: Primary 53C40
MathSciNet review: 0375173
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Abstract: An isometric immersion of an $ n$-dimensional compact Riemannian manifold with sectional curvature always less than $ {\lambda ^{ - 2}}$ into Euclidean space of dimension $ 2n - 1$ can never be contained in a ball of radius $ \lambda $. This generalizes and includes results of Tompkins and Chern and Kuiper.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0375173-3
Keywords: Isometric embedding, sectional curvature, Tompkin counter-example
Article copyright: © Copyright 1973 American Mathematical Society