Abstracts of the Arbeitsgruppenseminar

Prof. Bernd Ammann und Mitarbeiter, Zimmer 119

Thomas Leistner, Aidelaide, Australia

The Killing connection and the range of the Killing operator

Oct 30, 14:15

The prolongation of the Killing equation for vector fields gives rise to a connection, the Killing connection. It is a very useful tool when studying Killing vector fields.
As an example, we present a result about Killing vector fields of semi-Riemannian product manifolds.
On the other hand, the Killing connection can be used when analysing the range of the Killing operator. Here we show a generalisation to symmetric spaces of Calabi’s 2nd order differential operator that provides exact integrability conditions for the range of the Killing operator.
This is joint work with Federico Costanza, Mike Eastwood and Benjamin McMillan.

Jesse Ratzkin, Univ. Würzburg

Compactness of singular, constant Q-curvature metrics on punctured spheres

January 8th, 14:15

Branson's (fourth-order) Q-curvature is a scalar quantity behaving similarly to scalar curvature, except that the differential equation describing how it transforms under a conformal change is fourth order instead of second order. One result of this law governing the behavior of Q-curvature under a conformal change is that sequences of solutions can easily concentrate, leading one naturally to singular solutions. I will describe some recent work navigating the moduli space of singular constant Q-curvature metrics on a punctured sphere, in particular describing conditions under which subsets of the moduli space are compact. This is joint work with J. H. Andrade and J. M. do Ó.

Anton Galaev, Hradec Kralove, Czechia

Holonomy of some connections on Lorentzian manifolds

January 29th, 14:15

At the beginning I will shortly recall some results from theory of holonomy groups of the Levi-Civita connection on Riemannian and Lorentzian manifolds. Then I will explain recent results on the holonomy of metric connections with torsion. In particular, I will discuss the classification problem for naturally reductive homogeneous spaces. If the time allows, I will also discuss recent results about holonomy and related problems for Weyl connections in Lorentzian signature.

Back to the plan of the Arbeitsgruppenseminar

Bernd Ammann, 26.01.2024
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