New curvature conditions for the Bochner Technique

• 成果类型: Article
• 署名作者: Petersen, Peter; Wink, Matthias
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-01003-3
• 发表日期: 2021
• 页码: 33-54
• 关键词: positive curvature; RIEMANNIAN-MANIFOLDS; ricci flow; 4-manifolds; CLASSIFICATION; VARIETIES; operator; THEOREM

摘要

We show that manifolds with [n/2]-positive curvature operators are rational homology spheres. This follows from a more general vanishing and estimation theorem for the pth Betti number of closed n-dimensional Riemannian manifolds with a lower bound on the average of the lowest n - p eigenvalues of the curvature operator. This generalizes results due to D. Meyer, Gallot-Meyer, and Gallot.