

Complex analysis and mathematical physics
September 29, 2015 16:00–17:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)






SubRiemannian geometry on infinite dimensional manifolds
I. G. Markina^{} ^{} University of Bergen

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Abstract:
We start from the definition of an infinitedimensional
manifold with a specific choice of the underlying vector space for
developing the smooth calculus. Then we define Riemannian and
subRiemannian structures, and discuss the choice of a tool for studying
geodesics on infinitedimensional subRiemannian manifolds. We show
that, similarly to the finitedimensional 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.

