## Some Remarks on Harmonic Spaces

7th October 2009, 1600 MC206

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 *p*∈*M* 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.