, Volume 90, Issue 3, pp 275-278

On 3-dimensional asymptotically harmonic manifolds

Purchase on Springer.com

$39.95 / €34.95 / £29.95 *

* Final gross prices may vary according to local VAT.

Get Access

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