Closed geodesics and holonomies for Kleinian manifolds

Abstract

For a rank one Lie group G and a Zariski dense and geometrically finite subgroup $\Gamma$ of G, we establish equidistribution of holonomy classes about closed geodesics for the associated locally symmetric space. Our result is given in a quantitative form for real hyperbolic geometrically finite manifolds whose critical exponents are big enough. In the case when G=PSL(2, C), our results can be interpreted as the equidistribution of eigenvalues of $\Gamma$ in the complex plane. When $\Gamma$ is a lattice, this result was proved by Sarnak and Wakayama in 1999.

arXiv comment29 pages, Minor corrections are made from the printed version (GAFA,Vol 24 (2014) 1608-1636)

References in corpus (2)

• Effective bisector estimate with application to Apollonian circle packings
• Mixing of frame flow for rank one locally symmetric spaces and measure classification