K\"ahler manifolds with homothetic foliations by curves

TL;DR

This paper classifies certain compact K"ahler manifolds that have a special type of foliation by curves, focusing on those with homothetic properties and totally geodesic leaves.

Contribution

It provides a classification of compact, simply connected K"ahler manifolds with specific holomorphic, homothetic, and geodesic foliations by curves.

Findings

Classification of manifolds with the specified foliation properties

Characterization of the geometric structure of such manifolds

Conditions under which these foliations exist

Abstract

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.