Isometric embedding of a compact riemannian manifold into euclidean space

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Abstract

An isometric immersion of an n-dimensional compact Riemannian manifold with sectional curvature always less than λ−2 into Euclidean space of dimension 2n 1 can never be contained in a ball of radius λ. This generalizes and includes results of Tompkins and Chern and Kuiper.

Original languageEnglish (US)
Pages (from-to)245-246
Number of pages2
JournalProceedings of the American Mathematical Society
Volume40
Issue number1
DOIs
StatePublished - Sep 1973
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

Keywords

  • Disometric embedding
  • Sectional curvature
  • Tompkin counterexample

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