Geodesically equivalent metrics

Host Institution:

La Trobe University

Title of Seminar:

Geodesically equivalent metrics: on the crossroad of differential geometry, integrable systems and mathematical physics

Speaker's Name:

Prof Vladimir Matveev

Speaker's Institution:

University of Jena, Germany

Time and Date:

Monday 26 September, 2011, 1:00 PM AEST

Seminar 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.

Seminar Convenor:

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