, Volume 90, Issue 3, pp 275-278

On 3-dimensional asymptotically harmonic manifolds

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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.

Supported by Swiss National Science Foundation.
The author thanks Forschungsinstitut für Mathematik, ETH Zürich for its hospitality and support.
Received: 4 October 2007