Positive scalar curvature on foliations: the noncompact case
| Autor: | Su, Guangxiang, Zhang, Weiping |
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| Rok vydání: | 2019 |
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| Zdroj: | Advances in Mathematics, 410 (2022), 108699, 17 pages |
| Druh dokumentu: | Working Paper |
| Popis: | Let $(M,g^{TM})$ be a noncompact (not necessarily complete) enlargeable Riemannian manifold in the sense of Gromov-Lawson and $F$ an integrable subbundle of $T M$ . Let $k^F$ be the leafwise scalar curvature associated to $g^F=g^{TM}|_F$. We show that if either $TM$ or $F$ is spin, then ${\rm inf}(k^F)\leq 0$. This generalizes the famous result of Gromov-Lawson on enlargeable manifolds to the case of foliations. It also extends an ansatz of Gromov on hyper-Euclidean spaces to general enlargeable Riemannian manifolds, as well as recent results on compact enlargeable foliated manifolds due to Benameur-Heitsch et al to the noncompact situation. Comment: 14 pages, revised version to appear in Advances in Mathematics |
| Databáze: | arXiv |
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