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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 528, Pages 153–165 (Mi znsl7408)  

On the exponential mapping of geodesics in sub-Riemannian geometry

V. R. Krym

Saint Petersburg State University
References:
Abstract: 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.
Key words and phrases: sub-Riemannian geometry, admissible geodesics, abnormal geodesics, nonholonomic distributions.
Received: 03.11.2023
Document Type: Article
UDC: 514.752.8:514.764.2:514.774.8
Language: Russian
Citation: V. R. Krym, “On the exponential mapping of geodesics in sub-Riemannian geometry”, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Zap. Nauchn. Sem. POMI, 528, POMI, St. Petersburg, 2023, 153–165
Citation in format AMSBIB
\Bibitem{Kry23}
\by V.~R.~Krym
\paper On the exponential mapping of geodesics in sub-Riemannian geometry
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXXV
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 528
\pages 153--165
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7408}
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