Deformational rigidity of integrable metrics on the torus

Speaker. Joscha Henheik
Date. 14.02.23 at 3:30 pm

Abstract. It is conjectured that the only integrable metrics on the two-dimensional torus are so-called Liouville metrics, i.e. having line-element ds^2 = (f(x) + g(y)) (dx^2 + dy^2). In this talk, we discuss a deformative version of this conjecture: We consider integrable deformations of a (non-flat) Liouville metric in a conformal class and show that for a fairly large class of such deformations the deformed metric is again Liouville. In order to put our results in perspective, we review existing results about integrable metrics on the torus. This talk is based on arXiv: 2210.02961.