Archiv der Mathematik

, Volume 90, Issue 3, pp 275–278 | Cite as

On 3-dimensional asymptotically harmonic manifolds

Article

Abstract.

Let (M,g) be a complete, simply connected Riemannian manifold of dimension 3 without conjugate points. We show that M is a hyperbolic manifold of constant sectional curvature \(\frac{-h^{2}}{4}\), provided M is asymptotically harmonic of constant h > 0.

Mathematics Subject Classification (2000).

Primary 53C35 Secondary 53C25 

Keywords.

Asymptotic harmonic manifold horospheres 

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Copyright information

©  2008

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichWinterthurerstrasse 190Zürich
  2. 2.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia

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