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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive
SIGMA, 2020 Volume 16, 064, 10 pp. (Mi sigma1601)
This article is cited in 2 papers

The Bochner Technique and Weighted Curvatures

Peter Petersen, Matthias Wink

Department of Mathematics, University of California, 520 Portola Plaza, Los Angeles, CA, 90095, USA

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.

Keywords: Bochner technique, smooth metric measure spaces, Hodge theory.

MSC: 53B20, 53C20, 53C21, 53C23, 58A14

Received: May 22, 2020; in final form June 29, 2020; Published online July 9, 2020

Language: English

DOI: 10.3842/SIGMA.2020.064



Bibliographic databases:
ArXiv: 2005.02604

© Steklov Math. Inst. of RAS, 2025