Binet-Legendre metric

Host Institution:

La Trobe University

Title of Seminar:

Binet-Legendre metric

Speaker's Name:

Prof Vladimir Matveev

Speaker's Institution:

University of Jena, Germany

Time and Date:

Friday 15 March, 2.00 PM (AEDT)

Seminar Abstract:

I will explain a simple construction from elementary convex geometry that associates a Riemannian metric g_F (called the Binet-Legendre metric) to a given Finsler metric F on a smooth manifold M (I explain what is it). The transformation F → g_F is C0-stable and has good smoothness properties. The Riemannian metric g_F also behaves nicely under conformal or bi-Lipshitz deformation of the Finsler metric F that makes it a powerful tool in Finsler geometry. This will be illustrated by solving a number of named problems in Finsler geometry and giving short proofs of known results. In particular, we will answer a question of Matsumoto about local conformal mapping between two Minkowski spaces and will describe all the possible conformal self-maps and all self-similarities of a Finsler manifold. We will also classify all compact conformally flat Finsler manifolds and solve the conjecture of Deng and Hu on locally symmetric Finsler spaces.

Seminar Convenor:

This email address is being protected from spambots. You need JavaScript enabled to view it.

AGR IT support:

This email address is being protected from spambots. You need JavaScript enabled to view it.