Manno G. Projective symmetries and superintegrable metrics (abstract)

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Speaker: Giovanni Manno

Title: Projective symmetries and superintegrable metrics

In this seminar I will discuss 2-dimensional metrics admitting vector fields whose local flow preserves geodesic curves (projective symmetries). We shall see how to construct quadratic first integrals of the geodesic flow of metrics admitting projective symmetries, also relating such integrals with the notion of projective equivalence. Then we shall see that metrics with three projective symmetries are superintegrable, i.e., the space of the quadratic integrals of their geodesic flow is 4-dimensional. Time permitting, we shall give a classification of metrics admitting at least a projective symmetry.

Event: Local and Nonlocal Geometry of PDEs and Integrability, 8-12 October 2018, SISSA, Trieste, Italy.
The conference in honor of Joseph Krasil'shchik's 70th birthday.