New Curvature Conditions for the Bochner Technique
| Autor: | Petersen, Peter, Wink, Matthias |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Invent. Math. 224, 33-54 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00222-020-01003-3 |
| Popis: | We prove a vanishing and estimation theorem for the $p^{\text{th}}$-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. For example, in dimensions $n=5,6$ we obtain vanishing of the Betti numbers provided that the curvature operator is $3$-positive. As B\"ohm-Wilking observed, $3$-positivity of the curvature operator is not preserved by the Ricci flow. Comment: An edited version to appear in Invent. Math. Corollary 3.3 and Proposition 3.5 to be published elsewhere |
| Databáze: | arXiv |
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