10 Dec 2015; IMS (UiTø), room U1=A228. 14:05-14:55.

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

"Lichnerowicz-type theorems in projective and c-projective geometry for indefinite metrics"

A vector field on a Kähler manifold is called c-projective if its flow preserves the set of J-planar curves. These curves are defined by the property that the acceleration is complex proportional to the velocity (they can be considered as natural generalizations of geodesics in the Kähler setting). In this talk, I will present certain aspects of the proof of a recent result obtained jointly with A. Bolsinov and V. Matveev: on a closed connected Kähler manifold of arbitrary signature, any c-projective vector field is an affine vector field unless the manifold is complex projective space with the standard metric.

I will also explain how to prove the real analog in Lorentzian signature: a projective vector field, i.e. one sending geodesics to geodesics (considered as unparametrized curves), on a closed Lorentzian manifold is affine unless the curvature is constant. Both results have been known in the case of definite signature.