Weyl structures with positive Ricci tensor

✍ Scribed by B Alexandrov; S Ivanov

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 88 KB
• Volume: 18
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(03)00010-x

✦ Synopsis

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.