Eigenvalues of harmonic almost submersions

E. Loubeau; R. Slobodeanu

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arXiv · 0809.1656

Eigenvalues of harmonic almost submersions

E. Loubeau·R. Slobodeanu

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Abstract

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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BibTeX RIS

E. Loubeau, R. Slobodeanu. 2008-09-09. Eigenvalues of harmonic almost submersions. https://arxiv.org/abs/0809.1656

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