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International conference "Analysis and Singularities" dedicated to 70th anniversary of Vladimir Igorevich Arnold
August 23, 2007 09:00, Moscow
 


Singular curves and invariants of geometric structures

A. A. Agrachev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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A. A. Agrachev



Abstract: Given a submanifold $V$ of the tangnet bundle to a smooth manifold $M$, we consider “admissible curves” on $M$ whose velocities belong to V. Among examples are parametrized by the length curves on a Riemannian manifold and integral curves of a vector distribution. The boundary map sends a curve into its endpoints. “Singular curves” are critical points of the boundary map restricted to the space of admissible curves. They give nice and efficient tools for the investigation and classification of many intersting geometric structures.

Language: English

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