# On 3-dimensional asymptotically harmonic manifolds

Schroeder, V; Shah, H (2008). On 3-dimensional asymptotically harmonic manifolds. Archiv der Mathematik, 90(3):275-278.

## 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 <EquationSource Format="TEX"> $$frac{-h^{2}}{4}$$ </EquationSource> , provided M is asymptotically harmonic of constant h > 0.

## 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 <EquationSource Format="TEX"> $$frac{-h^{2}}{4}$$ </EquationSource> , provided M is asymptotically harmonic of constant h > 0.

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3 citations in Web of Science®
3 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English March 2008 13 Jan 2009 10:04 05 Apr 2016 12:39 Springer 0003-889X The original publication is available at www.springerlink.com https://doi.org/10.1007/s00013-008-2611-2 http://www.ams.org/mathscinet-getitem?mr=2391362http://arxiv.org/abs/0710.0740