Jet Berwald-Riemann-Lagrange Geometrization for Affine Maps between Finsler Manifolds

Abstract

In this paper we introduce a natural definition for the affine maps between two Finsler manifolds $(M,F)$ and $(N,\tilde{F})$ and we give some geometrical properties of these affine maps. Starting from the equations of the affine maps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jet space $J^1(TM;N)$, in the sense of a Berwald nonlinear connection ${\Gamma }_j^{b}et$, a Berwald ${\Gamma }_j^{b}et$-linear d-connection $B{\Gamma }_j^{b}et$, together with its d-torsions and d-curvatures, which geometrically characterizes the initial affine maps between Finsler manifolds.

arXiv comment22 pages