Conformal product structures on compact K\"ahler manifolds

TL;DR

This paper characterizes all compact Kähler manifolds that admit conformal product structures, which are special Weyl connections with reducible holonomy, providing a comprehensive geometric classification.

Contribution

It offers a complete geometric description of compact Kähler manifolds with conformal product structures, expanding understanding of Weyl connections in complex geometry.

Findings

Classification of compact Kähler manifolds with conformal product structures

Description of Weyl connections with reducible holonomy on these manifolds

Geometric characterization of conformal product structures

Abstract

A conformal product structure on a Riemannian manifold is a Weyl connection with reducible holonomy. We give the geometric description of all compact K\"ahler manifolds admitting conformal product structures