A horizontal endomorphism of the canonical superspray

Authors : Esmaeil Azizpour, Mohammad Hassan Zarifi

Pages : 18-24

Doi:10.33401/fujma.404797

View : 11 | Download : 9

Publication Date : 2018-06-30

Article Type : Research

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