The Bochner Technique and Weighted Curvatures

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2020
• Hauptverfasser: Petersen, Peter, Wink, Matthias
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210784
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: The Bochner Technique and Weighted Curvatures. Peter Petersen and Matthias Wink. SIGMA 16 (2020), 064, 10 pages

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