General Mathematics, Vol. 5, No. 1 - 4, pp. 339-346, 1995

Monica Purcaru -- On Transformation Groups of $ \boldsymbol N $-Linear Connections in the Bundle of Accelerations

Abstract: In the present paper we define the notion of transformation of $N$-linear connections in the bundle of accelerations $(Osc^2 M,\pi,M)$, we prove that the set $\cal T$ of the transformations of $N$-linear connections on $E=Osc^2 M$ together with the mapping composition is, in general, a non comutative group. In the group $\cal T$ there are some subgroups which keep invariant some of the components of an $N$- linear connection $D\Gamma (N)$ and $\cal T$ is a semidirect product of these subgroups. We study the transformation laws of the torsion and curvature tensor fields with respect to the transformations of the subgroup ${\cal T}_N$, that is the transformations of $N$-linear connections on $ E, $ which preserve the nonlinear connection N.

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