[en] On Sasakian manifolds with their naturally occurring sub-Riemannian structure, we consider parallel and mirror maps along geodesics of a taming Riemannian metric. We show that these transport maps have well-defined limits outside the sub-Riemannian cut-locus. Such maps are not related to parallel transport with respect to any connection. We use this map to obtain bounds on the second derivative of the sub-Riemannian distance. As an application, we get some preliminary result on couplings of sub-Riemannian Brownian motions.
Disciplines :
Mathematics
Author, co-author :
Baudoin, Fabrice; University of Connecticut - UCONN > Department of Mathematics
Grong, Erlend; University of Bergen > Department of Mathematics
Neel, Robert; Lehigh University > Department of Mathematics