A horizontal endomorphism of the canonical superspray

Year 2018, Volume: 1 Issue: 1, 18 - 24, 30.06.2018

Esmaeil Azizpour , Mohammad Hassan Zarifi

https://doi.org/10.33401/fujma.404797

https://izlik.org/JA29BK84AK

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.

Keywords

Horizontal endomorphism , Riemann-Finsler supermetric , Superspray

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