Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 064, 10 pages      arXiv:2005.02604      https://doi.org/10.3842/SIGMA.2020.064
Contribution to the Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday

The Bochner Technique and Weighted Curvatures

Peter Petersen and Matthias Wink
Department of Mathematics, University of California, 520 Portola Plaza, Los Angeles, CA, 90095, USA

Received May 22, 2020, in final form June 29, 2020; Published online July 09, 2020

Abstract
In this note we study the Bochner formula on smooth metric measure spaces. We introduce weighted curvature conditions that imply vanishing of all Betti numbers.

Key words: Bochner technique; smooth metric measure spaces; Hodge theory.

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