On harmonic and asymptotically harmonic homogeneous spaces

Details On harmonic and asymptotically harmonic homogeneous spaces On harmonic and asymptotically harmonic homogeneous spaces

2004-09-20

arxiv.org/abs/math/0409347v2

Mathematics

Differential Geometry

20 pages; final version

Scientific paper

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.

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