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- W2570354480 abstract "We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds to the case of foliated spin manifolds. As a consequence, we show that there is no foliation of positive leafwise scalar curvature on any torus, which generalizes the famous theorem of Schoen-Yau and Gromov-Lawson on the non-existence of metrics of positive scalar curvature on torus to the case of foliations. Moreover, our method, which is partly inspired by the analytic localization techniques of Bismut-Lebeau, also applies to give a new proof of the celebrated Connes vanishing theorem without using noncommutative geometry." @default.
- W2570354480 created "2017-01-13" @default.
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- W2570354480 date "2015-08-18" @default.
- W2570354480 modified "2023-09-27" @default.
- W2570354480 title "Positive scalar curvature on foliations" @default.
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- W2570354480 doi "https://doi.org/10.48550/arxiv.1508.04503" @default.
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