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

DOI:
https://doi.org/10.1090/S0002-9947-1986-0819950-4

MathSciNet review:
819950

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Abstract: Call a compact Riemannian manifold 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 contains elements of arbitrarily small energy. If is isometrically immersed in Euclidean space, then a condition on the second fundamental form of is given which implies 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0819950-4

Keywords:
Instability of harmonic maps,
symmetric spaces

Article copyright:
© Copyright 1986
American Mathematical Society