Geometry of bracket-generating distributions of step 2 on graded manifolds
A $Z_2-$graded analogue of bracket-generating distribution is given. Let $\cd$ be a distribution of rank $(p,q)$ on an $(m,n)$-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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2018-09-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/542746 |
| Summary: | A $Z_2-$graded analogue of bracket-generating distribution is given. Let $\cd$ be a distribution of rank $(p,q)$ on an $(m,n)$-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 $(m-p, n-q)$ on $\cm$. |
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| ISSN: | 2619-9653 |