On pluricanonical locally conformally K\"ahler manifolds

TL;DR

This paper provides a concise proof that compact pluricanonical locally conformally K"ahler manifolds necessarily have a parallel Lee form, clarifying a key geometric property.

Contribution

It offers a simplified proof of a known result regarding the parallelism of the Lee form in pluricanonical locally conformally K"ahler manifolds.

Findings

Compact pluricanonical locally conformally K"ahler manifolds have parallel Lee form

The proof simplifies understanding of their geometric structure

Clarifies the relationship between pluricanonical condition and Lee form properties

Abstract

We give a short proof of the fact that compact pluricanonical locally conformally K\"ahler manifolds have parallel Lee form.