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arXiv · 1703.03062

K\"ahler manifolds with geodesic holomorphic gradients

Andrzej Derdzinski·Paolo Piccione
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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.

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Andrzej Derdzinski, Paolo Piccione. 2017-03-08. K\"ahler manifolds with geodesic holomorphic gradients. https://doi.org/10.4171/rmi%2F1173

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