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Proceedings of the American Mathematical Society

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

 

 

A theorem on the tension field


Authors: Th. Koufogiorgos and Ch. Baikoussis
Journal: Proc. Amer. Math. Soc. 93 (1985), 321-324
MSC: Primary 58E20
DOI: https://doi.org/10.1090/S0002-9939-1985-0770545-5
MathSciNet review: 770545
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Abstract: Suppose $ M$ and $ N$ are complete Riemannian manifolds; $ M$ with Ricci curvature bounded from below and $ N$ with sectional curvature bounded from above by a constant $ {K_0}$. Let $ f:M \to N$ be a smooth map such that $ f(M) \subset {B_R}$, where $ {B_R}$ is a normal ball in $ N$ and furthermore $ R < \pi /2\sqrt {{K_0}} $ if $ {K_0} > 0$. If the energy density $ e(f)$ is bounded below by a positive constant, then there is a point $ P \in M$ such that the tension field $ \tau (f)$ at $ P$ is different from zero.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0770545-5
Article copyright: © Copyright 1985 American Mathematical Society