Weyl structures with positive Ricci tensor

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 pa...

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Bibliographic Details
Published in:arXiv.org 2003-01
Main Authors: Alexandrov, Bogdan, Ivanov, Stefan
Format: Article
Language:English
Subjects:
Mathematical analysis
Tensors
Online Access:Get full text
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Summary: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 \(q>1\).
ISSN:2331-8422