Spectral flow,Llarull's rigidity theorem in odd dimensions and its generalization

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外文摘要：For a compact spin Riemannian manifold(M,gTM)of dimension n such that the associated scalar curvature kTM verifies that kTM≥n(n-1),Llarull's rigidity theorem says that any area-decreasing smooth map f from M to the unit sphere Sn of nonzero degree is an isometry.In this paper,we present a new proof of Llarull's rigidity theorem in odd dimensions via a spectral flow argument.This approach also works for a generalization of Llarull's theorem when the sphere Sn is replaced by an arbitrary smooth strictly convex closed hypersurface inRn+1.The results answer two questions by Gromov(2023).

外文关键词：

Dirac operatorscalar curvaturespectral flow

作者：

Yihan Li、Guangxiang Su、Xiangsheng Wang

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作者单位：

Chern Institute of Mathematics & LPMC,Nankai University,Tianjin 300071,China

School of Mathematics,Shandong University,Jinan 250100,China

基金：

Nankai Zhide FoundationNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNankai Zhide FoundationFundamental Research Funds for the Central UniversitiesNational Natural Science Foundation of ChinaProject of Young Scholars of Shandong UniversityFundamental Research Funds of Shandong University

项目编号：

1227126611931007100-63233103121013612020GN063

出版年：

2024

DOI：

10.1007/s11425-023-2138-5

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(5)