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 Scopus®