Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures

Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures

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Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure.Then it is shown in (15), that, if saddam hussein propaganda poster the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space.In this paper, we provide an exposition on under armour 1364182 the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures.Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.