Dept Math & Stat UiT, Forskningsparken B459
  27 Sep 2021 Mon 13:00-14:00

Vladimir Matveev (Friedrich-Schiller-Universität Jena, Germany)

"Superintegrable metrics on surfaces"

The main result of the talk is that, under some nondegeneracy conditions, a 2-dimensional metric whose geodesic flow is superintegrable in the class of integrals which are polynomial in momenta is real analytic.

The first application is that every such superintegrable metric on the 2-sphere, such that one additional integral is quadratic in momenta, is a metric of constant positive curvature. The second application is that for any degree d there exists a metric on the sphere admitting an irreducible integral, which is polynomial in momenta of degree d, and admitting no more essential additional integral polynomial in momenta.