Eigenvalues of harmonic almost submersions

Details Eigenvalues of harmonic almost submersions Eigenvalues of harmonic almost submersions

2008-09-09

arxiv.org/abs/0809.1656v1

Mathematics

Differential Geometry

29 pages

Scientific paper

Maps between Riemannian manifolds which are submersions on a dense subset, are studied by means of the eigenvalues of the pull-back of the target metrics, the first fundamental form. Expressions for the derivatives of these eigenvalues yield characterizations of harmonicity, totally geodesic maps and biconformal changes of metric preserving harmonicity. A Schwarz lemma for pseudo harmonic morphisms is proved, using the dilatation of the eigenvalues and, in dimension five, a Bochner technique method, involving the Laplacian of the difference of the eigenvalues, gives conditions forcing pseudo harmonic morphisms to be harmonic morphisms.

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