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 |
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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 |
| _version_ | 1797350185155690496 |
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| author | Esmaeil Azizpour Dordi Mohammad Ataei |
| author_facet | Esmaeil Azizpour Dordi Mohammad Ataei |
| author_sort | Esmaeil Azizpour |
| collection | DOAJ |
| description | 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 $\cm$. |
| first_indexed | 2024-03-08T12:41:06Z |
| format | Article |
| id | doaj.art-27425de001f94c4fbc6f32e24c0b6a30 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:06Z |
| publishDate | 2018-09-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-27425de001f94c4fbc6f32e24c0b6a302024-01-21T11:14:53ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532018-09-011319620110.32323/ujma.4167411225Geometry of bracket-generating distributions of step 2 on graded manifoldsEsmaeil Azizpour0Dordi Mohammad Ataei1University of Guilan, Rasht, IranUniversity of Guilan, Rasht, IranA $Z_2-$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 $\cm$.https://dergipark.org.tr/tr/download/article-file/542746graded manifolddistribution |
| spellingShingle | Esmaeil Azizpour Dordi Mohammad Ataei Geometry of bracket-generating distributions of step 2 on graded manifolds Universal Journal of Mathematics and Applications graded manifold distribution |
| title | Geometry of bracket-generating distributions of step 2 on graded manifolds |
| title_full | Geometry of bracket-generating distributions of step 2 on graded manifolds |
| title_fullStr | Geometry of bracket-generating distributions of step 2 on graded manifolds |
| title_full_unstemmed | Geometry of bracket-generating distributions of step 2 on graded manifolds |
| title_short | Geometry of bracket-generating distributions of step 2 on graded manifolds |
| title_sort | geometry of bracket generating distributions of step 2 on graded manifolds |
| topic | graded manifold distribution |
| url | https://dergipark.org.tr/tr/download/article-file/542746 |
| work_keys_str_mv | AT esmaeilazizpour geometryofbracketgeneratingdistributionsofstep2ongradedmanifolds AT dordimohammadataei geometryofbracketgeneratingdistributionsofstep2ongradedmanifolds |