Adapted connections on metric contact manifolds
arXiv:1204.2972 · doi:10.1016/j.geomphys.2012.06.010
Abstract
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-forms, which splits into various subspaces. We study the parts of the torsion tensor according to this splitting to completely describe the space of adapted connections. We use this description to obtain characterizations of the generalized Tanaka-Webster connection and to describe the Dirac operators of adapted connections.
25 pages; some remarks added, minor corrections