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arXiv · 1402.4985

Curvature conditions for complex-valued harmonic morphisms

Jonas Nordström
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Abstract

We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form. We also give a necessary curvature condition for the existence of complex-valued harmonic morphisms with totally geodesic fibers on Einstein manifolds.

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Jonas Nordström. 2014-02-20. Curvature conditions for complex-valued harmonic morphisms. https://arxiv.org/abs/1402.4985

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