Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonexistence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of Euclidean space


Authors: Ralph Howard and S. Walter Wei
Journal: Trans. Amer. Math. Soc. 294 (1986), 319-331
MSC: Primary 58E20
MathSciNet review: 819950
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Call a compact Riemannian manifold $ M$ a strongly unstable manifold if it is not the range or domain of a nonconstant stable harmonic map and also the homotopy class of any map to or from $ M$ contains elements of arbitrarily small energy. If $ M$ is isometrically immersed in Euclidean space, then a condition on the second fundamental form of $ M$ is given which implies $ M$ is strongly unstable. As compact isotropy irreducible homogeneous spaces have "standard" immersions into Euclidean space this allows a complete list of the strongly unstable compact irreducible symmetric spaces to be made.


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


Similar Articles

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

Retrieve articles in all journals with MSC: 58E20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0819950-4
PII: S 0002-9947(1986)0819950-4
Keywords: Instability of harmonic maps, symmetric spaces
Article copyright: © Copyright 1986 American Mathematical Society