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Geodesics in Geometry with Constraints and Applications

  • Irina MarkinaEmail author
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 251)

Abstract

In this course we carefully define the notion of a non-holonomic manifold which is a manifold with a certain non-integrable distribution. We describe such concepts as horizontal distribution, the Ehresmann connection, bracket generating condition for a distribution, sub-Riemannian structure and sub-Riemannian metric, Hamiltonian system, normal and abnormal geodesics, principal bundle and others.

Keywords

Sub-Riemannian geometry non-holonomic constraints smooth manifold smooth sub-bundle principal bundle geodesic length minimisers Hamiltonian system rolling system controllability Carnot–Carathéodory distance 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway

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