El próximo jueves 16 de noviembre, a las 12.15 en la Sala de Juntas del Departamento de Matemáticas, Edificio Carlos Benítez, en la Facultad de Ciencias en Badajoz, el profesor Zdeněk Dušek del Institute of Technology and Business in České Budějovice impartirá la conferencia titulada «Geodesic orbit Finsler (α, β)-metrics» como Colloquium del Departamento.

Resumen: A homogeneous Riemannian or Finsler metric is called geodesic orbit metric if every geodesic is an orbit of a one-parameter group of isometries. There are many results about geodesic orbit manifolds in Riemannian geometry and currently there is increasing interest about them also in Finsler geometry. Currently we study the particular Finsler metrics, namely the (α, β)-metrics F , which arise from the Riemannian metric α and a one-form β. We introduce the concept of geodesic graph, which describes the structure of generators of the orbits in the Lie algebra of the isometry group. We prove the existence of a particular reductive decomposition for easy comparison of Finslerian geodesic graph with the Riemannian geodesic graph of the underlying Riemannian metric. As a consequence, we prove that for underlying geodesic orbit Riemannian metric α, all Finsler (α, β)-metrics F are also geodesic orbit metrics. We illustrate these constructions with metrics on spheres. As a corollary, geodesic orbit Finsler (α, β)-metrics F on spheres are determined. Part of this work is a joint work with Teresa Arias Marco.