Simplicial Volume of Closed Locally Homogeneous Riemannian Manifolds

2022/11/16 by Peng Hui How, How, P.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2211.09177

openalex publication_date 2022/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type.

Related

• Homotopy type and volume of locally symmetric manifolds
• Locally homogeneous RCD spaces
• Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one
• The spectrum of simplicial volume of non-compact manifolds
• Proportionality principle for the simplicial volume of families of Q-rank 1 locally symmetric spaces