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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
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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.

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Keywords: Instability of harmonic maps, symmetric spaces
Article copyright: © Copyright 1986 American Mathematical Society