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

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

2008-02-09

arxiv.org/abs/0802.1268v1

Mathematics

Differential Geometry

22 pages

Scientific paper

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 $\Gamma^b_jet$, a Berwald $\Gamma^b_jet$-linear d-connection $B\Gamma^b_jet$, together with its d-torsions and d-curvatures, which geometrically characterizes the initial affine maps between Finsler manifolds.

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