Fibrations and fundamental groups of Kaehler-Weyl manifolds

TL;DR

This paper extends a classical theorem to a special class of Kaehler--Weyl manifolds, revealing new restrictions on their fundamental groups and conditions under which they are actually Kaehler.

Contribution

It generalizes the Siu--Beauville theorem to Kaehler--Weyl manifolds and explores implications for their fundamental groups and Kähler properties.

Findings

Kaehler--Weyl manifolds fiber over hyperbolic Riemann surfaces under certain conditions

Restrictions on the fundamental groups of these manifolds are established

In some cases, these manifolds are shown to be genuinely Kaehler

Abstract

We extend the Siu--Beauville theorem to a certain class of compact Kaehler--Weyl manifolds, proving that they fiber holomorphically over hyperbolic Riemannian surfaces whenever they satisfy the necessary topological hypotheses. As applications we obtain restrictions on the fundamental groups of such Kaehler--Weyl manifolds, and show that in certain cases they are in fact Kaehler.