Research Article
BibTex RIS Cite

Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras

Year 2020, , 87 - 97, 15.10.2020
https://doi.org/10.36890/iejg.630746

Abstract

The classification of almost contact $B-$metric manifolds is considered. It is shown that $\mathcal{D}-$homothetic deformation of these manifolds in the class $\mathcal{F}_{i}$ $\left( i=0,1,4,5\right) $ remains in the same the class $\mathcal{F}_{i}$. We study almost contact $B-$metric structure on $5-$dimensional nilpotent Lie algebras. The class of the left invariant almost contact $B-$metric structures on corresponding Lie groups is investigated. Finally, we determine the class of $5-$dimensional nilpotent Lie algebras with almost contact $B-$metric structure.

References

  • [1] Bulut, Ş.: D-homothetic deformation on almost contact B-metric manifolds. J. of Geo. 110(23), (2019).
  • [2] Chinea, D., Gonzalez, C.: A classification of almost contact metric manifolds. An.Sti.Univ."Al.I.Cuza"Iasi. 30, 75-79 (1984).
  • [3] Dixmier, J.: Sur les representations unitaires des groupes de Lie nilpotentes III. Canadian Journal of Mathematics. 10, 321-348 (1958).
  • [4] Ganchev, G., Borisov, A.: Note on almost contact manifolds with Norden metric. Compt. Rend. Acad. Bulg. Sci. 39, 31-34 (1986).
  • [5] Ganchev, G., Mihova, V., Gribachev, K.: Almost contact manifolds with B-metric. Mathematica Balkanica. 7, 261-276 (1993).
  • [6] Manev, M.: Curvature properties on some classes of almost contact manifolds with B-metric. Compt. Rend. Acad. Bulg. Sci. 65 (4), 283-290 (2012).
  • [7] Manev, H.: On the structure tensors of almost of contact B-metric Manifolds. Filomat. 29(3), 427-436 (2015).
  • [8] Morimoto, A.: On normal almost contact structures. J. Math. Soc. Japan. 15, 420-436 (1963).
  • [9] Özdemir, N., Solgun, M., Aktay, Ş.: Almost contact metric structures on 5-dimensional nilpotent Lie algebras. Symmetry. 76(8), (2016).
Year 2020, , 87 - 97, 15.10.2020
https://doi.org/10.36890/iejg.630746

Abstract

References

  • [1] Bulut, Ş.: D-homothetic deformation on almost contact B-metric manifolds. J. of Geo. 110(23), (2019).
  • [2] Chinea, D., Gonzalez, C.: A classification of almost contact metric manifolds. An.Sti.Univ."Al.I.Cuza"Iasi. 30, 75-79 (1984).
  • [3] Dixmier, J.: Sur les representations unitaires des groupes de Lie nilpotentes III. Canadian Journal of Mathematics. 10, 321-348 (1958).
  • [4] Ganchev, G., Borisov, A.: Note on almost contact manifolds with Norden metric. Compt. Rend. Acad. Bulg. Sci. 39, 31-34 (1986).
  • [5] Ganchev, G., Mihova, V., Gribachev, K.: Almost contact manifolds with B-metric. Mathematica Balkanica. 7, 261-276 (1993).
  • [6] Manev, M.: Curvature properties on some classes of almost contact manifolds with B-metric. Compt. Rend. Acad. Bulg. Sci. 65 (4), 283-290 (2012).
  • [7] Manev, H.: On the structure tensors of almost of contact B-metric Manifolds. Filomat. 29(3), 427-436 (2015).
  • [8] Morimoto, A.: On normal almost contact structures. J. Math. Soc. Japan. 15, 420-436 (1963).
  • [9] Özdemir, N., Solgun, M., Aktay, Ş.: Almost contact metric structures on 5-dimensional nilpotent Lie algebras. Symmetry. 76(8), (2016).
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şenay Bulut 0000-0002-0317-1791

Sevgi Enveş Ermiş This is me 0000-0002-5523-3157

Publication Date October 15, 2020
Acceptance Date August 16, 2020
Published in Issue Year 2020

Cite

APA Bulut, Ş., & Enveş Ermiş, S. (2020). Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras. International Electronic Journal of Geometry, 13(2), 87-97. https://doi.org/10.36890/iejg.630746
AMA Bulut Ş, Enveş Ermiş S. Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras. Int. Electron. J. Geom. October 2020;13(2):87-97. doi:10.36890/iejg.630746
Chicago Bulut, Şenay, and Sevgi Enveş Ermiş. “Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie Algebras”. International Electronic Journal of Geometry 13, no. 2 (October 2020): 87-97. https://doi.org/10.36890/iejg.630746.
EndNote Bulut Ş, Enveş Ermiş S (October 1, 2020) Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras. International Electronic Journal of Geometry 13 2 87–97.
IEEE Ş. Bulut and S. Enveş Ermiş, “Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras”, Int. Electron. J. Geom., vol. 13, no. 2, pp. 87–97, 2020, doi: 10.36890/iejg.630746.
ISNAD Bulut, Şenay - Enveş Ermiş, Sevgi. “Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie Algebras”. International Electronic Journal of Geometry 13/2 (October 2020), 87-97. https://doi.org/10.36890/iejg.630746.
JAMA Bulut Ş, Enveş Ermiş S. Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras. Int. Electron. J. Geom. 2020;13:87–97.
MLA Bulut, Şenay and Sevgi Enveş Ermiş. “Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie Algebras”. International Electronic Journal of Geometry, vol. 13, no. 2, 2020, pp. 87-97, doi:10.36890/iejg.630746.
Vancouver Bulut Ş, Enveş Ermiş S. Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras. Int. Electron. J. Geom. 2020;13(2):87-9.