On harmonic and asymptotically harmonic homogeneous spaces

Jens Heber

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arXiv · math/0409347

On harmonic and asymptotically harmonic homogeneous spaces

Jens Heber

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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.

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BibTeX RIS

Jens Heber. 2005-10-04. On harmonic and asymptotically harmonic homogeneous spaces. https://arxiv.org/abs/math/0409347

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