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Autore principale: Ma, Junyu
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2402.18141
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author Ma, Junyu
author_facet Ma, Junyu
contents It was proved by Gromov-Lawson\cite{gl83} that complete three manifold with positive scalar curvature bounded below has finite Urysohn 1-width only depends on the uniform positive scalar curvature bounds. It is natural to ask the same question for the four manifolds. In this paper, we can show that closed four and five manifolds with positive biRicci curvature has finite Urysohn 1-width only depends on the curvature bounds. During the proof we can also observe that the fundamental group of those manifolds are virtually free. This gives a quick application that $T^{2}\times S^{2}$ can't admit positive biRicci curvature.
format Preprint
id arxiv_https___arxiv_org_abs_2402_18141
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Urysohn 1-width for 4 and 5 manifolds with positive biRicci curvature
Ma, Junyu
Differential Geometry
53C12
It was proved by Gromov-Lawson\cite{gl83} that complete three manifold with positive scalar curvature bounded below has finite Urysohn 1-width only depends on the uniform positive scalar curvature bounds. It is natural to ask the same question for the four manifolds. In this paper, we can show that closed four and five manifolds with positive biRicci curvature has finite Urysohn 1-width only depends on the curvature bounds. During the proof we can also observe that the fundamental group of those manifolds are virtually free. This gives a quick application that $T^{2}\times S^{2}$ can't admit positive biRicci curvature.
title Urysohn 1-width for 4 and 5 manifolds with positive biRicci curvature
topic Differential Geometry
53C12
url https://arxiv.org/abs/2402.18141