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Complex analysis and mathematical physics
September 29, 2015 16:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)
 


Sub-Riemannian geometry on infinite dimensional manifolds

I. G. Markina

University of Bergen

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Abstract: We start from the definition of an infinite-dimensional manifold with a specific choice of the underlying vector space for developing the smooth calculus. Then we define Riemannian and sub-Riemannian structures, and discuss the choice of a tool for studying geodesics on infinite-dimensional sub-Riemannian manifolds. We show that, similarly to the finite-dimensional case, there are two different, but not mutually disjoint classes of geodesics. We present geodesic equations for those classes of geodesics which are natural generalisations of classical Riemannian geodesics.

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