Asymptotically harmonic manifolds without focal points

Abstract

In this note we show that a compact asymptotically harmonic manifold without focal points is either flat or a rank one locally symmetric space.

arXiv comment8 pages (v2: revised introduction, minor changes)

References in corpus (2)

• New results on noncompact harmonic manifolds
• On 3-dimensional asymptotically harmonic manifolds with minimal horospheres

Cited by in corpus (2)

• Volume entropy rigidity of non-positively curved symmetric spaces
• Geometry of Asymptotically harmonic manifolds with minimal horospheres