# Some Remarks on Harmonic Spaces

7th October 2009, 1600 MC206

Professor Werner Ballman

from

The Max-Planck-Institute and the University of Bonn

will speak on

Some Remarks on Harmonic Spaces

By definition, a Riemannian manifold M is called harmonic, if each point pM has a neigborhood U such that there is a non-constant harmonic function on U\p. Euclidean spaces and, more generally, two-point homogeneous spaces are harmonic. Conversely, the so-called Lichnerowicz conjecture states that any complete and simply connected harmonic manifold is two-point homogeneous. This was proved by Szabó in the compact case, in the non-compact case, Damek and Ricci found counterexamples. I will discuss the compact case.