2004/09/20 by Jens Heber, Heber, Jens · 1 citation
Mathematics · Physics and Astronomy · #53C24 #53C30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.math/0409347
openalex publication_date 2004/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.