A compactness theorem for locally homogeneous spaces

2019/11/12 by Pediconi, Francesco
#53C21 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.05062

Abstract

We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature |sec|≤ 1. Moreover, we show that the set of geometric models is compact in the pointed C^1,α-topology.

Related

• Homogeneous locally compact spaces
• Convergence of locally homogeneous spaces
• Compactness Theorem of Complete k-Curvature Manifolds with Isolated Singularities
• Local structure of homogeneous ANR-spaces
• Separation of homogeneous connected locally compact spaces