Geodesic
The Schouten curvature and the Jacobi equation in sub-Riemannian geometry
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 121-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that if a distribution does not depend on the vertical coordinates, then the Schouten curvature tensor coincides with the Riemannian curvature. The Schouten curvature tensor and the nonholonomicity tensor are used to write the Jacobi equation for the distribution. This leads to a study of second-order optimality conditions for horizontal geodesics in sub-Riemannian geometry. We study conjugate points for horizontal geodesics on the Heisenberg group as an example. 
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V. R. Krym. The Schouten curvature and the Jacobi equation in sub-Riemannian geometry. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 121-134. http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a8/

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