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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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:March 2008
Deposited On:13 Jan 2009 10:04
Last Modified:05 Apr 2016 12:39
Publisher:Springer
ISSN:0003-889X
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00013-008-2611-2
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2391362
http://arxiv.org/abs/0710.0740

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