Mathematics – Differential Geometry
Scientific paper
1999-02-04
Mathematics
Differential Geometry
8 pages, Latex format, no figures; added section; to appear in Diff. Geom. Appl
Scientific paper
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 $q>1$.
Alexandrov Bogdan
Ivanov Stefan
No associations
LandOfFree
Weyl structures with positive Ricci tensor does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Weyl structures with positive Ricci tensor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weyl structures with positive Ricci tensor will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-232340