A report on locally conformally K\"ahler manifolds

TL;DR

This paper reviews recent advances in locally conformally K"ahler geometry, emphasizing topological obstructions to their existence on compact manifolds.

Contribution

It provides a comprehensive overview of recent results and highlights the topological conditions that prevent certain manifolds from admitting locally conformally K"ahler structures.

Findings

Identification of key topological obstructions

Summary of recent classification results

Insights into the structure of locally conformally K"ahler manifolds

Abstract

We present an overview of recent results in locally conformally K\"ahler geometry, with focus on the topological properties which obstruct the existence of such structures on compact manifolds.