On harmonic and asymptotically harmonic homogeneous spaces

By Jens Heber. 2004

66 citations recorded by the source corpus.

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].

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8fb7bd13456f7f2e3431a009ab4f8f24e968b2c2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Jorge Lauret
2. Michael Jablonski
3. Ramiro A. Lafuente
4. Anna Fino
5. Tracy L. Payne
6. Romina M. Arroyo
7. V. Manero
8. M. Fernández

In Astronomy and Astrophysics

1. Jorge Lauret
2. Michael Jablonski
3. Ramiro A. Lafuente
4. Tracy L. Payne

In Geometry and Topology

1. Jorge Lauret
2. Michael Jablonski
3. Ramiro A. Lafuente
4. Anna Fino
5. Tracy L. Payne
6. Romina M. Arroyo
7. V. Manero
8. M. Fernández

Citations in the corpus

• Einstein solvmanifolds and nilsolitons (2008, background): “• [Heber 06] All harmonic noncompact homogeneous manifolds are stan- dard solvmanifolds (with dim a = 1).”