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The paper shows that if the distribution is defined on a manifold with the special smooth structure and does not depend on the vertical coordinates, then the Schouten curvature tensor coincides with the Riemannian curvature tensor. The Schouten curvature tensor is used to write the Jacobi equation for the distribution. This leads to studies on second-order optimality conditions for the horizontal geodesics in subRiemannian geometry. Conjugate points are defined by the solutions of the Jacobi equation. If a geodesic passed a point conjugated with its beginning then this geodesic ceases to be optimal
Translated title of the contributionКривизна Схоутена неголономного распределения в субримановой геометрии и поля Якоби
Original languageEnglish
Title of host publicationOPTA-SCL 2018 - Proceedings of the School-Seminar on Optimization Problems and their Applications
Pages213-227
StatePublished - 2018
EventШкола-семинар по проблемам оптимизации и их применению - Омск, Омск, Russian Federation
Duration: 8 Jul 201814 Jul 2018

Publication series

NameCEUR WORKSHOP PROCEEDINGS
Volume2098

Conference

ConferenceШкола-семинар по проблемам оптимизации и их применению
Abbreviated titleOPTA-SCL 2018
Country/TerritoryRussian Federation
CityОмск
Period8/07/1814/07/18

ID: 127455878