Discrete Groups and Non-Riemannian Homogeneous Spaces

Discrete Groups and Non-riemannian Homogeneous Spaces

A basic question in geometry is to understand compact locally homogeneous manifolds, i.e., those compact manifolds that can be locally modelled on a homogeneous space J\H of a finite-dimensional Lie group H. This means that there is an atlas on a manifold M consisting of local diffeomorphisms with open sets in J\H where the transition functions between these open sets are given by translations ...

6 On discontinuous group actions on non - Riemannian homogeneous spaces ∗

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudoRiemannian manifolds with constant curvatures, and discuss what kind of problems we propose to pursue. For pseudo-Riemannian manifolds, isometric acti...

On discontinuous group actions on non-Riemannian homogeneous spaces

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudoRiemannian manifolds with constant curvatures, and discuss what kind of problems we propose to pursue. For pseudo-Riemannian manifolds, isometric acti...

On Riemannian Curvature of Homogeneous Spaces

The Kinematic Formula in Riemannian Homogeneous Spaces

Let G be a Lie group and K a compact subgroup of G. Then the homogeneous space G/K has an invariant Riemannian metric and an invariant volume form ΩG. Let M and N be compact submanifolds of G/K, and I(M ∩ gN) an “integral invariant” of the intersection M ∩ gN . Then the integral