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Steklov Mathematical Institute Seminar
October 25, 2001, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)
 


Use of the inverse problem method for solving certain classical problems of differential geometry

V. E. Zakharov

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Abstract: By using the dressing method, which is a modern version of the inverse problem method, it is possible to solve the following classical problems of differential geometry.
1. Classification of $N$-orthogonal curvilinear coordinate systems in Euclidean space and in a space of constant curvature. (Formulated in 1813 by Binnet and Dupin.)
2. Description of spaces of flat connections together with their embedding in a Euclidean space.

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