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Isometric immersion of a compact Riemannian manifold into a Euclidean space

Published online by Cambridge University Press:  17 April 2009

Sharief Deshmukh
Sharief Deshmukh
Affiliation:
Department of Mathematics, King Saud University, PO Box 2455 Riyadh 11451, Saudi Arabia
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Abstract

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We show that an isometric immersion of an n−dimensional compact Riemannian manifold of non-negative Ricci curvature with scalar curvature always less than n(n−1)λ−2 into a Euclidean space of dimension n + 1 can never be contained in a ball of radius λ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 2 , October 1992 , pp. 177 - 178
Copyright
Copyright © Australian Mathematical Society 1992

References

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