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arXiv · 2212.07715

Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling

Fabrice Baudoin·Erlend Grong·Robert Neel·Anton Thalmaier
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Abstract

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.

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Fabrice Baudoin, Erlend Grong, Robert Neel, Anton Thalmaier. 2022-12-15. Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling. https://arxiv.org/abs/2212.07715

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