Research Article
BibTex RIS Cite
Year 2018, , 196 - 201, 30.09.2018
https://doi.org/10.32323/ujma.416741

Abstract

References

  • [1] A. Bejancu, On bracket-generating distributions, Int. Electron. J. Geom. 3 (2010) no. 2, 102 - 107.
  • [2] O. Goertsches, Riemannian supergeometry, Math. Z., 260 (2008) 557-–593.
  • [3] J. Monterde and J. Munoz-Masque and O. A. Sanchez-Valenzuela, Geometric properties of involutive distributions on graded manifolds, Indag. Mathem., N.S., 8 (1997), 217-246.
  • [4] S. Vacaru and H. Dehnen, Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity, Gen. Rel. Grav., 35 (2003) 209-250.
  • [5] S. I. Vacaru, Superstrings in higher order extensions of Finsler Superspaces, Nucl. Phys. B 494 (1997) no. 3, 590-656.
  • [6] V. S. Varadarajan, Supersymmetry for mathematicians: an introduction, Courant Lecture Notes Series, New York, 2004.
  • [7] P. C. West, Introduction to supersymmetry and supergravity, Second Edition, World Scientific Pub Co Inc, 1990.
  • [8] C. D. Zanet, Generic one-step bracket-generating distributions of rank four, Archivum Mathematicum, 51 (2015), 257 - 264.

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

Year 2018, , 196 - 201, 30.09.2018
https://doi.org/10.32323/ujma.416741

Abstract

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 $\cm$.

References

  • [1] A. Bejancu, On bracket-generating distributions, Int. Electron. J. Geom. 3 (2010) no. 2, 102 - 107.
  • [2] O. Goertsches, Riemannian supergeometry, Math. Z., 260 (2008) 557-–593.
  • [3] J. Monterde and J. Munoz-Masque and O. A. Sanchez-Valenzuela, Geometric properties of involutive distributions on graded manifolds, Indag. Mathem., N.S., 8 (1997), 217-246.
  • [4] S. Vacaru and H. Dehnen, Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity, Gen. Rel. Grav., 35 (2003) 209-250.
  • [5] S. I. Vacaru, Superstrings in higher order extensions of Finsler Superspaces, Nucl. Phys. B 494 (1997) no. 3, 590-656.
  • [6] V. S. Varadarajan, Supersymmetry for mathematicians: an introduction, Courant Lecture Notes Series, New York, 2004.
  • [7] P. C. West, Introduction to supersymmetry and supergravity, Second Edition, World Scientific Pub Co Inc, 1990.
  • [8] C. D. Zanet, Generic one-step bracket-generating distributions of rank four, Archivum Mathematicum, 51 (2015), 257 - 264.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Esmaeil Azizpour

Dordi Mohammad Ataei This is me

Publication Date September 30, 2018
Submission Date April 18, 2018
Acceptance Date September 24, 2018
Published in Issue Year 2018

Cite

APA Azizpour, E., & Ataei, D. M. (2018). Geometry of bracket-generating distributions of step 2 on graded manifolds. Universal Journal of Mathematics and Applications, 1(3), 196-201. https://doi.org/10.32323/ujma.416741
AMA Azizpour E, Ataei DM. Geometry of bracket-generating distributions of step 2 on graded manifolds. Univ. J. Math. Appl. September 2018;1(3):196-201. doi:10.32323/ujma.416741
Chicago Azizpour, Esmaeil, and Dordi Mohammad Ataei. “Geometry of Bracket-Generating Distributions of Step 2 on Graded Manifolds”. Universal Journal of Mathematics and Applications 1, no. 3 (September 2018): 196-201. https://doi.org/10.32323/ujma.416741.
EndNote Azizpour E, Ataei DM (September 1, 2018) Geometry of bracket-generating distributions of step 2 on graded manifolds. Universal Journal of Mathematics and Applications 1 3 196–201.
IEEE E. Azizpour and D. M. Ataei, “Geometry of bracket-generating distributions of step 2 on graded manifolds”, Univ. J. Math. Appl., vol. 1, no. 3, pp. 196–201, 2018, doi: 10.32323/ujma.416741.
ISNAD Azizpour, Esmaeil - Ataei, Dordi Mohammad. “Geometry of Bracket-Generating Distributions of Step 2 on Graded Manifolds”. Universal Journal of Mathematics and Applications 1/3 (September 2018), 196-201. https://doi.org/10.32323/ujma.416741.
JAMA Azizpour E, Ataei DM. Geometry of bracket-generating distributions of step 2 on graded manifolds. Univ. J. Math. Appl. 2018;1:196–201.
MLA Azizpour, Esmaeil and Dordi Mohammad Ataei. “Geometry of Bracket-Generating Distributions of Step 2 on Graded Manifolds”. Universal Journal of Mathematics and Applications, vol. 1, no. 3, 2018, pp. 196-01, doi:10.32323/ujma.416741.
Vancouver Azizpour E, Ataei DM. Geometry of bracket-generating distributions of step 2 on graded manifolds. Univ. J. Math. Appl. 2018;1(3):196-201.

 23181

Universal Journal of Mathematics and Applications 

29207              

Creative Commons License  The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.