Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
MathSciNet review: 560590
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C42

Retrieve articles in all journals with MSC: 53C42

Additional Information

Keywords: Isometric immersion, scalar curvature, sectional curvature, complete Riemannian manifold
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society