A horizontal endomorphism of the canonical superspray

Abstract

Giving up the homogeneity condition of a Lagrange superfunction, we prove that there is a unique horizontal endomorphism $h$ (nonlinear connection) on a supermanifold ${\mathcal{M}},$ such that $h$ is conservative and its torsion vanishes. There are several examples for nonhomogeneous Lagrangians such that this result is not true.