Weyl structures with positive Ricci tensor
Abstract
We prove the vanishing of the first Betti number on compact manifolds admitting a Weyl structure whose Ricci tensor satisfies certain positivity conditions, thus obtaining a Bochner-type vanishing theorem in Weyl geometry. We also study compact Hermitian-Weyl manifolds with non-negative symmetric part of the Ricci tensor of the canonical Weyl connection and show that every such manifold has first Betti number
b
1
=1
and Hodge numbers
h
p,0
=0
for
p>0
,
h
0,1
=1
,
h
0,q
=0
for
q>1
.