K\"ahler manifolds with geodesic holomorphic gradients
Differential Geometry
2023-09-12 v1
Abstract
A vector field on a Riemannian manifold is called geodesic if its integral curves are reparametrized geodesics. We classify compact K\"ahler manifolds admitting nontrivial real-holomorphic geodesic gradient vector fields that satisfy an additional integrability condition. They are all biholomorphic to bundles of complex projective spaces.
Keywords
Cite
@article{arxiv.1703.03062,
title = {K\"ahler manifolds with geodesic holomorphic gradients},
author = {Andrzej Derdzinski and Paolo Piccione},
journal= {arXiv preprint arXiv:1703.03062},
year = {2023}
}
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52 pages