29 Apr 2011; IMS (UiTø), room U1=A228. Friday 12:15-14:00.

Stefan Roseman (Friedrich-Schiller-Universität Jena, Germany)

Yano-Obata conjecture for holomorph-projective transformations

Given a Kähler manifold, one associates a class of distinguished curves to the Kähler metric which are called h(olomorphically)-planar curves. Such curves can be seen as some kind of generalization of geodesics on Kähler manifolds.

One problem of interest is to understand whether the group of holomorph-projective transformations (i.e. the group of all bi-holomorphic mappings which preserve the set of all h-planar curves) is really bigger than the group of holomorphic isometries of the Kähler manifold.

We have proven a classical conjecture attributed to Yano and Obata stating that on a compact, connected Riemannian Kähler manifold, the connected components of both groups coincide unless the metric has constant positive holomorphic sectional curvature.

The work is joint with V.S. Matveev.