Finslerian Approach Based on the Concept of Osculation

Abstract

In theoretical physics the equations of physical fields are formulated in terms of Lagrangian scalar densities which are assumed to be functions of the field variables and, perhaps, auxiliary fields, both depending on xⁱ alone. In attempting to exploit the potentialities of Finsler geometry with the aim of generalizing the equations of physical fields, one is faced with the new circumstance that the Finslerian generalizations of Lagrangian densities will involve a dependence on the tanget vector yⁱ treated as a directional variable essentially independent of the positional argument xⁱ.