Weyl structures with positive Ricci tensor

1999/02/04 by Bogdan Alexandrov, Stefan Ivanov, Alexandrov, Bogdan +1
Mathematics · Physics and Astronomy · #53C15 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C15 #msc:53C55

paper · pdf · doi:10.48550/arxiv.math/9902033

8 pages, Latex format, no figures; added section; to appear in Diff. Geom. Appl

openalex publication_date 1999/02/04 · arxiv created 2003/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 b₁ =1 and Hodge numbers h^p,0 =0 for p>0, h^0,1 =1, h^0,q =0 for q>1.

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