10 Sep 2015; IMS (UiTø), room U1=A228. 14:15-15:15.

Vladimir Matveev (Friedrich-Schiller-Universität Jena, Germany)

“Conformally Berwald manifolds, special  holonomy, and compact quotients of incomplete reducible  manifolds”

In the first part of the talk I will explain a trick that reduces many problems in the Finsler geometry to problems in Riemannian geometry. Then I will show two relatively easy applications, both joint results with Marc Troyanov (EPF Lausanne): one based on the Riemannian holonomy theory and the other on the theory of homogenous manifolds. Finally I discuss a joint result with Yury Nikolayevsky (La Trobe Melbourne) - we reformulate the initial Finsler problem as the following Riemannian problem: describe compact quotients  of incomplete locally reducible Riemannian manifolds by homotheties. This is a classical an well-studied  problem, I will give an  overview of the known results, present some new, and derive implications for the initial Finsler problem.