$\mathrm{K}$-cowaist on complete foliated manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909767051509760 |
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| author | Su, Guangxiang Wang, Xiangsheng |
| author_facet | Su, Guangxiang Wang, Xiangsheng |
| contents | 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 the $\widehat{\mathrm{A}}$-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 $\inf(k^F)\leq 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_08354 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | $\mathrm{K}$-cowaist on complete foliated manifolds Su, Guangxiang Wang, Xiangsheng Differential Geometry 58J20, 53C21, 53C12 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 the $\widehat{\mathrm{A}}$-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 $\inf(k^F)\leq 0$. |
| title | $\mathrm{K}$-cowaist on complete foliated manifolds |
| topic | Differential Geometry 58J20, 53C21, 53C12 |
| url | https://arxiv.org/abs/2107.08354 |