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)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, North-Holland Math. Library, vol. 9, North-Holland, Amsterdam, 1975. MR 0458335 (56:16538)
  • [2] J. Eells, Jr. and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1-68. MR 495450 (82b:58033)
  • [3] Th. Hasanis and D. Koutroufiotis, Immersion of bounded mean curvature, Arch. Math. 33 (1979), 170-171. MR 557750 (80m:53045)
  • [4] H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. MR 0215259 (35:6101)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58E20

Retrieve articles in all journals with MSC: 58E20


Additional Information

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

American Mathematical Society