NEW TOOLS IN FINSLER GEOMETRY: STRETCH AND RICCI SOLITONS

Firstly, the notion of stretch from Riemannian geometry is extended to Finsler spaces in relationship with the smoothness function of Ohta and the reversibility function of Rademacher. As an application, the Sphere Theorem of Rademacher is rewritten in terms of stretch for the case of Randers and Matsumoto metrics by pointed out the usual Riemannian pinching constant 1/4. Secondly, one put in evidence a strong relationship, induced by the Zermelo navigation problem, between Randers metrics of constant flag curvature and Ricci solitons.