Killing potentials with geodesic gradients on K\"ahler surfaces

TL;DR

This paper classifies certain compact K"ahler surfaces where the gradient flows of specific functions are reparametrized geodesics, revealing new geometric structures and properties.

Contribution

It provides a classification of K"ahler surfaces with Killing potentials whose gradient integral curves are geodesics, a novel geometric characterization.

Findings

Classification of such K"ahler surfaces achieved

Identification of conditions for gradient curves to be geodesics

New insights into the structure of Killing potentials on K"ahler surfaces

Abstract

We classify compact K\"ahler surfaces with nonconstant Killing potentials such that all integral curves of their gradients are reparametrized geodesics.