Differential Geometry Working Seminar

Jacques Van Wyk, University of Waterloo

“The” Generalised Levi-Civita Connection

I will discuss the notions of generalised metrics and generalised connections in generalised geometry. A generalised connection has an associated torsion tensor, so one may ask, if given a generalised metric G, whether there is a torsion-free connection D compatible with G; this is the analogue of the Levi-Civita connection. We will see that there are infinitely many such connections D, that is, there is no unique “generalised Levi-Civita connection,” a striking difference from the situation for Riemannian geometry.

MC 5479