Geodesics in Geometry with Constraints and Applications
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.
KeywordsSub-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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