Shortest and straightest geodesics in sub-Riemannian geometry

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Shortest and straightest geodesics in sub-Riemannian geometry

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Shortest and straightest geodesics in sub-Riemannian geometry

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of geometry and physics

ISSN

0393-0440

e-ISSN

—

Svazek periodika

155

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

"Article Number: 103713"

Kód UT WoS článku

000551647000003

EID výsledku v databázi Scopus

2-s2.0-85085325694