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

Fabrice Baudoin; Erlend Grong; Robert Neel; Anton Thalmaier

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

Fabrice Baudoin, Erlend Grong, Robert Neel, Anton Thalmaier

Publikation: Working paper/Preprint › Preprint

31 Downloads (Pure)

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.

Originalsprog	Udefineret/Ukendt
Udgiver	ArXiv
Status	Udgivet - dec. 2022
Udgivet eksternt	Ja

Emneord

math.DG
math.PR
60D05, 53C17, 58J65

Adgang til dokumentet

2212.07715v1

Citationsformater

@misc{e978db877d3946e884dd4c9ba88e9aed,

title = "Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling",

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.",

keywords = "math.DG, math.PR, 60D05, 53C17, 58J65",

author = "Fabrice Baudoin and Erlend Grong and Robert Neel and Anton Thalmaier",

note = "15 pages",

year = "2022",

month = dec,

language = "Udefineret/Ukendt",

publisher = "ArXiv",

type = "WorkingPaper",

institution = "ArXiv",

}

TY - UNPB

T1 - Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling

AU - Baudoin, Fabrice

AU - Grong, Erlend

AU - Neel, Robert

AU - Thalmaier, Anton

N1 - 15 pages

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

KW - math.DG

KW - math.PR

KW - 60D05, 53C17, 58J65

M3 - Preprint

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

PB - ArXiv

ER -