Archiv der Mathematik

, Volume 90, Issue 3, pp 275–278

On 3-dimensional asymptotically harmonic manifolds

Authors

    • Institut für MathematikUniversität Zürich
  • Hemangi Shah
    • School of MathematicsTata Institute of Fundamental Research
Article

DOI: 10.1007/s00013-008-2611-2

Cite this article as:
Schroeder, V. & Shah, H. Arch. Math. (2008) 90: 275. doi:10.1007/s00013-008-2611-2

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 53C35Secondary 53C25

Keywords.

Asymptotic harmonic manifoldhorospheres

Copyright information

©  2008