Spiro Karigiannis, University of Waterloo
Infinitesimal deformations of G-structures
I will introduce the setting of G-structures on an oriented Riemannian n-manifold, where G is a closed Lie subgroup of SO(n). These can be understood in terms of global sections of the SO(n) bundle which is the quotient of the SO(n)-prinicipal bundle of oriented orthonormal frames by the free action of G. We will define the intrinsic torsion of a G-structure, and explain how to describe infinitesimal deformations of G-structures. If time permits, we will discuss a Dirichlet energy type of functional on the space of G-structures, whose critical points are called harmonic G-structures. This condition includes the torsion-free G-structures but is more general. These ideas were developed recently by Fowdar, Loubeau, Moreno, Sa Earp building on earlier work in the G2 and Spin(7) cases by myself from 2006-2007.
MC 5479