$\mathrm{K}$-cowaist on complete foliated manifolds
| Autor: | Su, Guangxiang, Wang, Xiangsheng |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $(M,F)$ be a connected (not necessarily compact) foliated manifold carrying a complete Riemannian metric $g^{TM}$. We generalize Gromov's $\mathrm{K}$-cowaist using the coverings of $M$, as well as defining a closely related concept called $\widehat{\mathrm{A}}$-cowaist. Let $k^F$ be the associated leafwise scalar curvature of $g^F = g^{TM}|_F$. We obtain some estimates on $k^F$ using these two concepts. In particular, assuming that the generalized $\mathrm{K}$-cowaist is infinity and either $TM$ or $F$ is spin, we show that $\inf(k^F)\leq 0$. Comment: 14 pages, 1 picture, major revision, add a discussion about the definitions of $\widehat{\mathrm{A}}$-cowaist and more details about the proof of the main theorem, comments are welcome! |
| Databáze: | arXiv |
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