Entropy and Arithmetic Quotients for Simple Automorphism Groups of Geometric Manifolds

Abstract

Let G be a connected simple Lie group, and suppose G acts on a compact real analytic manifold M. Assume that G preserves a unimodular rigid geometric structure, for example a connection and a volume form. The aim of this paper is to describe the measure theoretic structure of such actions, when ℝ-rank(G)≥2.