The 11th DIFFERENTIAL GEOMETRY DAY

at LUND

Wednesday the 20th of May 2015


ABSTRACTS

Lars Andersson (Albert Einstein Institute - Potsdam, DE) Geometry and analysis in black hole spacetimes The dynamical stability of the Kerr rotating black hole spacetime is one of the central open problems in general relativity. The Carter constant plays a key role in understanding the stability problem. I will explain how the Carter constant arises and discuss how it and related symmetry operators enters in the analysis of the dynamics of geodesics, waves and Maxwell fields on the Kerr background. Andrew Swann (Aarhus University, DK) HyperKähler manifolds with a circle symmetry The Gibbons-Hawkins ansatz provides a local description all four-dimensional hyperKähler manifolds with a circle symmetry in terms of harmonic functions in R^3. This talk will show how potential theory may be used to provide a full classification of complete examples with or without finite topological type. Time permitting, I will also discuss how closely related ideas may be used to construct examples in higher dimensions and what can be said about their local structure. Andreas Arvanitoyeorgos (University of Patras, GR) Recent progress on homogeneous Einstein metrics Ilka Agricola (Universität Marburg, DE) Classification of naturally reductive spaces We present a new method for classifying naturally reductive homogeneous spaces, i. e. homogeneous Riemannian manifolds admitting a metric connection with skew torsion that has parallel torsion and curvature. This method is based on a deeper understanding of the holonomy algebra of connections with parallel skew torsion on Riemannian manifolds and the interplay of such a connection with the geometric structure on the given Riemannian manifold. It allows to reproduce by easier arguments the known classifications in dimensions 3, 4, and 5, and yields as a new result the classification in dimension 6. In each dimension, one obtains a "hierarchy" of degeneracy for the torsion form, which we then treat case by case. For the completely degenerate cases, we obtain results that are independent of the dimension. In some situations, we are able to prove that any Riemannian manifold with parallel skew torsion has to be naturally reductive. We show that a "generic" parallel torsion form defines a quasi-Sasakian structure in dimension 5 and an almost complex structure in dimension 6.