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.References
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Additional Information
- Jens Heber
- Affiliation: Mathematisches Seminar, Universität Kiel, 24098 Kiel, Germany
- Email: heber@math.uni-kiel.de
- Gerhard Knieper
- Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
- MR Author ID: 103300
- Email: Gerhard.Knieper@rub.de
- Hemangi M. Shah
- Affiliation: Department of Mathematics, Indian Institute of Technology, Powai, Mumbai 400076, India
- Email: hema@math.iitb.ac.in
- Received by editor(s): April 19, 2005
- Received by editor(s) in revised form: October 3, 2005
- Published electronically: August 31, 2006
- Additional Notes: All three authors were supported in part by DFG priority program “Global Differential Geometry" (SPP 1154)
- Communicated by: Jon G. Wolfson
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 845-849
- MSC (2000): Primary 53C35; Secondary 53C25
- DOI: https://doi.org/10.1090/S0002-9939-06-08520-0
- MathSciNet review: 2262881