Compact asymptotically harmonic manifolds
Differential Geometry
2012-10-17 v2 Dynamical Systems
Abstract
A complete Riemannian manifold without conjugate points is called asymptotically harmonic if the mean curvature of its horospheres is a universal constant. Examples of asymptotically harmonic manifolds include flat spaces and rank one locally symmetric spaces of noncompact type. In this paper we show that this list exhausts the compact asymptotically harmonic manifolds under a variety of assumptions including nonpositive curvature or Gromov hyperbolic fundamental group. We then present a new characterization of symmetric spaces amongst the set of all visibility manifolds
Keywords
Cite
@article{arxiv.1205.2271,
title = {Compact asymptotically harmonic manifolds},
author = {Andrew M. Zimmer},
journal= {arXiv preprint arXiv:1205.2271},
year = {2012}
}
Comments
24 pages (v2: minor changes including renumbering theorems to reflect published version). Final version to appear in Journal of Modern Dynamics