# 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.