From rotations of conics to a class of Riemann-Finslerian flows

Abstract

The aim of this paper is to produce new examples of (semi-) Riemannian and Finsler structures in dimension two having as model a scalar deformation of conics which generalizes the rotation with a right angle. It continues [6] and [8] from the point of view of relationship between quadratic polynomials (which provide equations of conics in dimension 2 and Finsler geometries. A type of two-dimensional Finslerian flow is introduced, based on the previous deformation and we completely solve the corresponding particular case of Riemannian flow.