Curvature conditions for complex-valued harmonic morphisms
Differential Geometry
2014-11-03 v2
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.
Cite
@article{arxiv.1402.4985,
title = {Curvature conditions for complex-valued harmonic morphisms},
author = {Jonas Nordström},
journal= {arXiv preprint arXiv:1402.4985},
year = {2014}
}
Comments
9 pages, new title and abstract, new Section 5 with new results