Asymptotically harmonic spaces in dimension 3

Heber, Jens; Knieper, Gerhard; Shah, Hemangi

doi:10.1090/S0002-9939-06-08520-0

Asymptotically harmonic spaces in dimension 3
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by Jens Heber, Gerhard Knieper and Hemangi M. Shah PDF

Proc. Amer. Math. Soc. 135 (2007), 845-849 Request permission

Abstract:

Let $M$ be a Hadamard manifold of dimension $3$ whose sectional curvature satisfies $-b^2 \le K \le -{a^2}< 0$ and whose curvature tensor satisfies $\Vert \nabla R\Vert \le C$ for suitable constants $0<a\le b$ and $C\ge 0$. We show that $M$ is of constant sectional curvature provided $M$ is asymptotically harmonic. This was previously only known if $M$ admits a compact quotient.

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