On harmonic and asymptotically harmonic homogeneous spaces |
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Authors: | J Heber |
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Institution: | 1. Mathematisches Seminar, Christian-Albrechts-Universit?t Kiel, Ludewig-Meyn-Str. 4, D – 24098, Kiel, Germany
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Abstract: | We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or rank-one symmetric, or a nonsymmetric
Damek–Ricci space. Independently, Y. Nikolayevsky has obtained the latter classification under the additional assumption of
nonpositive sectional curvatures N2].
Supported in part by DFG priority program “Global Differential Geometry” (SPP 1154).
Received: September 2004; Revision: June 2005; Accepted: September 2005 |
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Keywords: | Homogeneous spaces harmonic manifolds asymptotically harmonic manifolds Einstein manifolds solvable Lie groups Matrix Riccati equation hypergeometric functions |
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