Isometric embedding of a compact riemannian manifold into euclidean space

Howard Jacobowitz

doi:10.1090/S0002-9939-1973-0375173-3

Isometric embedding of a compact riemannian manifold into euclidean space

Howard Jacobowitz

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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 language	English (US)
Pages (from-to)	245-246
Number of pages	2
Journal	Proceedings of the American Mathematical Society
Volume	40
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1973-0375173-3
State	Published - Sep 1973
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Disometric embedding
Sectional curvature
Tompkin counterexample

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10.1090/S0002-9939-1973-0375173-3

Cite this

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title = "Isometric embedding of a compact riemannian manifold into euclidean space",

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.",

keywords = "Disometric embedding, Sectional curvature, Tompkin counterexample",

author = "Howard Jacobowitz",

year = "1973",

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KW - Disometric embedding

KW - Sectional curvature

KW - Tompkin counterexample

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Isometric embedding of a compact riemannian manifold into euclidean space

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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