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arXiv · 2601.12461

Homological $k$-systole in $n$-manifolds with positive intermediate curvature

Jingche Chen·Han Hong
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Abstract

In this paper, we prove optimal $k$-systolic inequalities and characterize the case of equality on closed $n$-dimensional Riemannian manifolds with positive intermediate curvature for $3\leq n\leq 7$. This unifies prior works of Bray-Brendle-Neves \cite{BrayBrenleNevesrigidity} and Chu-Lee-Zhu \cite{chuleezhu_n_systole}, and extends them to higher codimensions. The proof is inspired by our recent work on splitting theorems under intermediate curvature \cite{chenhong2026}.

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BibTeXRIS

Jingche Chen, Han Hong. 2026-01-18. Homological $k$-systole in $n$-manifolds with positive intermediate curvature. https://arxiv.org/abs/2601.12461

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