MAXIMAL FIRST BETTI NUMBER RIGIDITY OF NONCOMPACT RCD(0,N) SPACES

被引：0

作者：

Ye, Zhu ^{[1
]}

机构：

[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 12期

基金：

北京市自然科学基金; 中国国家自然科学基金;

关键词：

METRIC-MEASURE-SPACES; RICCI CURVATURE; GEOMETRY;

D O I：

10.1090/proc/16574

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (M, d, m) be a noncompact RCD(0,N) space with N E N+ , suppm = M. We prove that if the first Betti number of M equals N - 1, then (M, d, m) is either a flat Riemannian N-manifold with a soul TN-1 or the metric product [0, oo) x TN-1, both with the measure a multiple of the N-dimensional Hausdorff measure itN, where TN-1 is a flat torus.

引用

页码：5403 / 5412

页数：10

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