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arXiv · 1404.5698

Closed geodesics and holonomies for Kleinian manifolds

Gregory Margulis·Amir Mohammadi·Hee Oh
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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.

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Gregory Margulis, Amir Mohammadi, Hee Oh. 2014-04-23. Closed geodesics and holonomies for Kleinian manifolds. https://arxiv.org/abs/1404.5698

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