A gradient-type deformation of conics and a class of Finslerian flows

Abstract

The aim of this paper is to produce new examples of Riemannian and Finsler structures having as model a scalar deformation of conics inspired by the scaling transformation. It continues [4] from the point of view of relationship between quadratic polynomials (which provide equations of conics in dimension 2) and Finsler geometries. A type of Finslerian ow is introduced, based on the previous deformation and we completely solve the corresponding particular case of Riemannian flow.

Keywords

• conic
• invariant
• finsler fundamental function
• deformation
• finslerian flow
• primary 53c60
• secondary 51mb04