Stability of Harmonic Morphisms
نویسنده
چکیده
We study the stability of harmonic morphisms as a subclass of harmonic maps. As a general result we show that any harmonic morphism to a manifold of dimension at least three is stable with respect to some Riemannian metric on the target. Furthermore we link the index and nullity of the composition of harmonic morphisms with the index and nullity of the composed maps.
منابع مشابه
Stability of Harmonic Morphisms to a Surface
Using the fact that harmonic morphisms to a surface have minimal bres, links between the volume-stability of the bres and the energy-stability of the map are found for manifolds without boundary. A stability result for harmonic morphisms from a manifold with boundary to a Riemann surface is also established.
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[A] M. Svensson, On holomorphic harmonic morphisms, Manuscripta Math. 107 (2002), 1–13. [B] M. Svensson, Harmonic morphisms from even-dimensional hyperbolic spaces, Math. Scand. 92 (2003), 246–260. [C] M. Svensson, Holomorphic foliations, harmonic morphisms and the Walczak formula, J. London Math. Soc. 68 (2003), 781–794. [D] M. Svensson, Harmonic morphisms in Hermitian geometry, J. Reine Angew...
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