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Asymptotically harmonic spaces in dimension 3
Author(s):
Jens
Heber;
Gerhard
Knieper;
Hemangi
M.
Shah
Journal:
Proc. Amer. Math. Soc.
135
(2007),
845-849.
MSC (2000):
Primary 53C35;
Secondary 53C25
Posted:
August 31, 2006
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Abstract:
Let  be a Hadamard manifold of dimension  whose sectional curvature satisfies  and whose curvature tensor satisfies  for suitable constants  and  . We show that  is of constant sectional curvature provided  is asymptotically harmonic. This was previously only known if  admits a compact quotient.
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Additional Information:
Jens
Heber
Affiliation:
Mathematisches Seminar, Universit{ät} Kiel, 24098 Kiel, Germany
Email:
heber@math.uni-kiel.de
Gerhard
Knieper
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
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
DOI:
10.1090/S0002-9939-06-08520-0
PII:
S 0002-9939(06)08520-0
Keywords:
Asymptotically harmonic manifold,
horospheres,
asymptotic geodesics.
Received by editor(s):
April 19, 2005
Received by editor(s) in revised form:
October 3, 2005
Posted:
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 of article:
Copyright
2006,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article M. Brin, Ergodic theory of frame flows, In: A. Katok (ed), Ergodic theory and dynamical systems, II (College Park, Md., 1979/1980), Progr. Math., Birkhäuser, Boston, 21 (1982), 163-183. (English) MR MR 0670078 (83m:58059)
J.-H. Eschenburg, E. Heintze, Comparison theory for Riccati equations, Manuscripta Math. 68 (1990), 209-214. (English) MR MR 1063226 (91d:34034)
G. Knieper, Spherical means on compact Riemannian manifolds of negative curvature, Differential Geom. Appl. 4 (1994), 361-390. (English) MR MR 1306567 (95i:58141)
Jens Heber, Gerhard Knieper, Hemangi M. Shah, Asymptotically harmonic spaces in dimension 3, Proceedings of the American Mathematical Society (3) 135 (2007), 845-849. (English) MR MR2262881
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