The ergodic theory of discrete isometry groups on manifolds of variable negative curvature

Hyperbolic Manifolds, Discrete Groups and Ergodic Theory

1 Ergodic theory References for this section: CFS]. 1. The basic setting of ergodic theory: a measure-preserving transformation T of a probability space (X; B; m). Usually we assume T is invertible. (More generally, measure-preserving means R f T = R f; equivalently, m(T ?1 (A)) = mA.) How many measure spaces are there? Standard Borel spaces: any Borel subset of a complete, separable metric spa...

Hyperbolic manifolds , discrete groups and ergodic theory

ISOMETRY GROUPS OF k-CURVATURE HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS

We study the isometry groups of a family of complete p + 2curvature homogeneous pseudo-Riemannian metrics on R which have neutral signature (3 + 2p, 3 + 2p), and which are 0-curvature modeled on an indecomposible symmetric space.

ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...