Equidistribution of holonomy restricted to a homology class about closed geodesics

Abstract

The purpose of this paper is, for each homology class, to prove the equidistribution theorem of restricted holonomy classes about closed geodesics mainly for the real hyperbolic manifolds. More precisely, this work is a continuation of the study [SW] (Duke Math. J. 100 (1999), 1–57) but one restricts these holonomy classes to the ones arising from the subset of closed geodesics whose corresponding hyperbolic conjugacy classes belong to a given homology class of the manifold. As an application, we also discuss the equidistribution of (imaginary) quadratic forms with respect to the argument of fundamental units. 1991 Mathematical Subject Classification. Primary 22; Secondary 53.