Geometry of bracket-generating distributions of step 2 on graded manifolds

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Universal Journal of Mathematics and Applications
Volume:1 Issue:3
Geometry of bracket-generating distributions of step 2 on graded manifolds

Geometry of bracket-generating distributions of step 2 on graded manifolds

Authors : Esmaeil AZİZPOUR, Dordi Mohammad ATAEİ

Pages : 196-201

Doi:10.32323/ujma.416741

View : 64 | Download : 6

Publication Date : 2018-09-30

Article Type : Research Paper

Abstract :A $Z_2-$graded analogue of bracket-generating distribution is given. Let $\cd$ be a distribution of rank $insert ignore into journalissuearticles values(p,q);$ on an $insert ignore into journalissuearticles values(m,n);$-dimensional graded manifold $\cm,$ we attach to $\cd$ a linear map $F$ on $\cd$ defined by the Lie bracket of graded vector fields of the sections of $\cd.$ Then $\mathcal{D}$ is a bracket-generating distribution of step $2$, if and only if $F$ is of constant rank $insert ignore into journalissuearticles values(m-p, n-q);$ on $\cm$.
Keywords : Graded manifold, Distribution

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