The 12th DIFFERENTIAL GEOMETRY DAY

at LUND

Wednesday the 18th of May 2016


ABSTRACTS

Thomas Bruun Madsen (Aarhus University, DK) SU(3)-invariant special geometry: rigidity and deformations I shall discuss invariant special geometry on simply-connected compact manifolds with a cohomogeneity one action of SU(3). My main focus will be geometries defined by a closed quaternionic 4-form. This talk is based on joint work with Diego Conti and Simon Salamon. Anna Sakovich (Uppsala University, SE) On geometric foliations and center of mass in mathematical general relativity The notion of center of mass is a very important and effective tool for describing the overall dynamics of a physical system. While in Newton's theory of gravity center of mass is straightforwardly defined via the mass density, the situation in general relativity is much more complicated. In this talk we will describe how to define the center of mass of asymptotically Euclidean and asymptotically hyperbolic manifolds using foliations by constant mean curvature surfaces (as first proposed by Huisken and Yau in 1996) and discuss the relation of this construction to Hamiltonian formulation of general relativity. Then we will present a new approach to defining the center of mass of asymptotically Euclidean initial data sets for the Einstein equations which serve as models for isolated systems in general relativity. This is joint work with Carla Cederbaum and Julien Cortier. Laurent Hauswirth (Université Paris Est, Marne-la-Vallée, FR) Surface theory in homogeneous 3-space I will give an introduction to the differential geometry of curves and surfaces in Thurston's homogeneous 3-manifolds with a particular scope on the role of harmonic map in the theory of constant mean curvature surfaces and minimal surfaces. Christoph Böhm (Westfälisches Wilhelms-Universität Münster, DE) Homogeneous Einstein metrics We will discuss general structure results for compact and non-compact homogeneous Einstein manifolds. In low dimensions classification results can be deduced. In higher dimensions we will address the major open problems.