Integrable LCK manifolds

TL;DR

This paper investigates integrable locally conformally Kähler (LCK) manifolds, characterizing unimodular LCK Lie algebras as Kähler Lie algebras with specific derivations, thus advancing understanding of their geometric structure.

Contribution

It introduces the class of integrable LCK manifolds and provides a characterization of unimodular integrable LCK Lie algebras in terms of Kähler Lie algebras and derivations.

Findings

Characterization of unimodular integrable LCK Lie algebras as Kähler Lie algebras with derivations

Introduction of integrable LCK manifolds as a natural class

Connection between anti-Lee form integrability and Lie algebra structure

Abstract

We study a natural class of LCK manifolds that we call integrable LCK manifolds: those where the anti-Lee form $\eta$ corresponds to an integrable distribution. As an application we obtain a characterization of unimodular integrable LCK Lie algebras as K\"ahler Lie algebras equipped with suitable derivations.