Complex homothetic foliations on K\"ahler manifolds

TL;DR

This paper classifies complex homothetic foliations on Kähler manifolds and uses this to construct special Ricci-flat metrics with specific curvature properties.

Contribution

It provides a local classification of complex homothetic foliations on Kähler manifolds and constructs new Ricci-flat metrics with particular curvature features.

Findings

Classification of complex homothetic foliations on Kähler manifolds

Construction of almost Kähler, Ricci-flat metrics

Identification of additional curvature properties

Abstract

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.