7th October 2009, 1600 MC206
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.