Семинар Математички методи механике, 5. октобар 2011.

• 03. Октобар, 2011
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Наредни састанак Семинара одржаће се у среду, 5. октобра 2011. у сали 301ф МИ САНУ са почетком у 14 часова.

Предавач: Владимир Матвејев (Универзитет Јена, Немачка)


Наслов предавања: ГЕОДЕЗИЈСКИ ЕКВИВАЛЕНТНЕ МЕТРИКЕ: НА РАСКРШЋУ ДИФЕРЕНЦИЈАЛНЕ ГЕОМЕТРИЈЕ, ИНТЕГРАБИЛНИХ СИСТЕМА И МАТЕМАТИЧКЕ ФИЗИКЕ


Abstract:

Can two different metrics have the same geodesics? Yes! The first examples were constructed already by Lagrange, and different versions of the question were actively studied by virtually all differential geometers 100 years ago. During my talk I will explain the solution of the Lie Problem which is the infinitesimal version of the question above; this is a joint result with R. Bryant and G. Manno), of the Beltrami Problem (which is presicely the question above, my contribution is to solve it on closed manifolds), and of the Lichnerowicz-Obata conjecture (which suggests an answer to Schouten problem). There are three main tools of the proof: integrable systems, geometric theory of partial differential equations and singularity theory.