Fibrations and fundamental groups of Kähler–Weyl manifolds

Abstract

We extend the Siu–Beauville theorem to a certain class of compact Kähler–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 Kähler–Weyl manifolds, and we show that in certain cases they are in fact Kähler.