Geodesic
On the exponential mapping of geodesics in sub-Riemannian geometry
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 153-165

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The equations of admissible geodesics for a nonholonomic distribution on Riemannian manifold are written in the mixed bundle. The differential of the exponential mapping for a nonholonomic distribution with the cyclicity condition for vertical coordinates is calculated. This differential is non-degenerate if the distribution is strongly bracket generating. The equations of admissible geodesics on 3-dimensional Lie groups are studied. 
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     author = {V. R. Krym},
     title = {On the exponential mapping of geodesics in {sub-Riemannian} geometry},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {153--165},
     publisher = {mathdoc},
     volume = {528},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a9/}
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V. R. Krym. On the exponential mapping of geodesics in sub-Riemannian geometry. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 153-165. http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a9/