Locally homogeneous RCD spaces

2024/04/03 by Honda, Shouhei, Nepechiy, Artem
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2404.02390

Abstract

The goal of this note is to demonstrate how existing results can be adapted to establish the following result: A locally metric measure homogeneous RCD(K,N) space is isometric to, after multiplying a positive constant to the reference measure, a smooth Riemannian manifold with the Riemannian volume measure.

Related

• Compact harmonic RCD(K, N) spaces are harmonic manifolds
• Volume entropy and rigidity for RCD-spaces
• Homogeneous locally compact spaces
• Simplicial Volume of Closed Locally Homogeneous Riemannian Manifolds
• From almost smooth spaces to RCD spaces