Esmaeil AZİZPOUR, Mohammad Hassan ZARİFİ

A horizontal endomorphism of the canonical superspray

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.

Keywords:

Horizontal endomorphism Riemann-Finsler supermetric, Superspray,

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