Seminar talk, 15 February 2017

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Speaker: Yuri Sachkov

Title: Cut loci in (sub-)Riemannian geometry

A sub-Riemannian structure on a manifold M is a subdistribution \Delta of the tangent distribution TM together with a metric g on the distribution \Delta. sub-Riemannian shortest paths and geodesics are defined in the same way as Riemannian, with admissible curves being tangent to the distribution \Delta. A cut point on a (sub-)Riemannian geodesic is the point at which a geodesic ceases to be shortest. The set of cut points along all geodesics starting from a fixed point is called a cut locus.

The talk will discuss a method of computation of the cut locus for left invariant sub-Riemannian structures on Lie groups and describe the results obtained by this method for sub-Riemannian problems on Lie groups SO(3), SL(2), SE(2), SH(2), and the Engel group.