Shortest and straightest geodesics in sub-Riemannian geometry

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017243" target="_blank" >RIV/62690094:18470/20:50017243 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0393044020300954?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0393044020300954?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2020.103713" target="_blank" >10.1016/j.geomphys.2020.103713</a>

Result language
angličtina
Original language name
Shortest and straightest geodesics in sub-Riemannian geometry
Original language description
There are several different, but equivalent definitions of geodesics in a Riemannian manifold, based on two characteristic properties: geodesics as shortest curves and geodesics as straightest curves. They are generalized to sub-Riemannian manifolds, but become non-equivalent. We give an overview of different approaches to the definition, study and generalization of sub-Riemannian geodesics and discuss interrelations between different definitions. For Chaplygin transversally homogeneous sub-Riemannian manifold Q, we prove that straightest geodesics (defined as geodesics of the Schouten partial connection) coincide with shortest geodesics (defined as the projection to Q of integral curves (with trivial initial covector) of the sub-Riemannian Hamiltonian system). This gives a Hamiltonization of Chaplygin systems in non-holonomic mechanics. We consider a class of homogeneous sub-Riemannian manifolds, where straightest geodesics coincide with shortest geodesics, and give a description of all sub-Riemannian symmetric spaces in terms of affine symmetric spaces. (C) 2020 Published by Elsevier B.V.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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