Homological $(n-2)$-systole in $n$-manifolds with positive triRic curvature
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914263183917056 |
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| author | Chen, Jingche Hong, Han |
| author_facet | Chen, Jingche Hong, Han |
| contents | In this paper, we prove an optimal systolic inequality and characterize the case of equality on closed Riemannian manifolds with positive triRic curvature. This extends prior work of Bray-Brendle-Neves \cite{BrayBrenleNevesrigidity} and Chu-Lee-Zhu \cite{chuleezhu_n_systole} to higher codimensions. The proof relies on the notion of stable weighted $k$-slicing, a weighted volume comparison theorem and metric-deformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12461 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homological $(n-2)$-systole in $n$-manifolds with positive triRic curvature Chen, Jingche Hong, Han Differential Geometry 53C21, 53C24 In this paper, we prove an optimal systolic inequality and characterize the case of equality on closed Riemannian manifolds with positive triRic curvature. This extends prior work of Bray-Brendle-Neves \cite{BrayBrenleNevesrigidity} and Chu-Lee-Zhu \cite{chuleezhu_n_systole} to higher codimensions. The proof relies on the notion of stable weighted $k$-slicing, a weighted volume comparison theorem and metric-deformation. |
| title | Homological $(n-2)$-systole in $n$-manifolds with positive triRic curvature |
| topic | Differential Geometry 53C21, 53C24 |
| url | https://arxiv.org/abs/2601.12461 |