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Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras

Year 2020, Volume: 3 Issue: 2, 175 - 184, 15.12.2020

Nilüfer Özdemir Mehmet Solgun Şirin Aktay

https://doi.org/10.33401/fujma.800222
Cited By: 4

Abstract

In this manuscript, almost para-contact metric structures on 5 dimensional nilpotent Lie algebras are studied. Some examples of para-Sasakian and para-contact structures on five-dimensional nilpotent Lie algebras are given.

Keywords

Almost para-contact metric structure 5-dimensional nilpotent Lie algebra Para-Sasakian structure

References

  • [1] S. Kaneyuki, F. L. Williams, Almost paracontact and Parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • [2] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom., (2009) 36:37. https://doi.org/10.1007/s10455-008-9147-3.
  • [3] G. Nakova, S. Zamkovoy, Almost paracontact manifolds, arXiv:0806.3859v2.
  • [4] S. Zamkovoy, On Para-Kenmotsu manifolds, arXiv:1711.03008v1.
  • [5] G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2) (2011), 697-718.
  • [6] G. Calvaruso, A. Perrone, Five-dimensional paracontact Lie algebras, Differ. Geom. Appl., 45 (2016), 115-129.
  • [7] . Kr Chaubey, S. Kr Yadav, Study of Kenmotsu manifolds with semi-symmetric metric connection, Univers. J. Math. Appl., 1(2) (2018), 89-97.
  • [8] A. Zaitov, D. Ilxomovich Jumaev, Hyperspaces of superparacompact spaces and continuous maps, Univers. J. Math. Appl. 2(2) (2019), 65-69.
  • [9] S. Zamkovoy, G. Nakova, The decomposition of almost paracontact metric manifolds in eleven classes revisited, J. Geom. (2018) 109:18. https://doi.org/10.1007/s00022-018-0423-5. [10] A. Andrada, A. Fino, L. Vezzoni, A class of Sasakian 5-manifolds, Transform Groups, 14(3) (2009),493-512.
  • [11] G. Calvaruso, A. Fino, Five-dimensional K-contact Lie algebras, Monatsh Math., 167 (2012).
  • [12] J. Dixmier, Sur les Repr ´ esentations unitaires des groupes de Lie nilpotentes III, Canad. J. Math., 10 (1958), 321-348.
  • [13] N. Özdemir, M. Solgun, Ş. Aktay, Quasi-Sasakian structures on 5-dimensional nilpotent Lie algebras, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019), 326-333.
  • [14] N. Özdemir, M. Solgun, Ş. Aktay, Almost contact metric structures on 5- dimensional nilpotent Lie algebras, Symmetry, 8(8) (2016), 76.
  • [15] M. P. Gong, Classification of Nilpotent Lie Algebras of Dimension 7, Ph.D. Thesis, University of Waterloo, Waterloo, Ontario, Canada, 1998.
  • [16] W. A. De Graaf, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra, 309 (2007), 640-653.

Year 2020, Volume: 3 Issue: 2, 175 - 184, 15.12.2020

Nilüfer Özdemir Mehmet Solgun Şirin Aktay

https://doi.org/10.33401/fujma.800222
Cited By: 4

Abstract

References

  • [1] S. Kaneyuki, F. L. Williams, Almost paracontact and Parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • [2] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom., (2009) 36:37. https://doi.org/10.1007/s10455-008-9147-3.
  • [3] G. Nakova, S. Zamkovoy, Almost paracontact manifolds, arXiv:0806.3859v2.
  • [4] S. Zamkovoy, On Para-Kenmotsu manifolds, arXiv:1711.03008v1.
  • [5] G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2) (2011), 697-718.
  • [6] G. Calvaruso, A. Perrone, Five-dimensional paracontact Lie algebras, Differ. Geom. Appl., 45 (2016), 115-129.
  • [7] . Kr Chaubey, S. Kr Yadav, Study of Kenmotsu manifolds with semi-symmetric metric connection, Univers. J. Math. Appl., 1(2) (2018), 89-97.
  • [8] A. Zaitov, D. Ilxomovich Jumaev, Hyperspaces of superparacompact spaces and continuous maps, Univers. J. Math. Appl. 2(2) (2019), 65-69.
  • [9] S. Zamkovoy, G. Nakova, The decomposition of almost paracontact metric manifolds in eleven classes revisited, J. Geom. (2018) 109:18. https://doi.org/10.1007/s00022-018-0423-5. [10] A. Andrada, A. Fino, L. Vezzoni, A class of Sasakian 5-manifolds, Transform Groups, 14(3) (2009),493-512.
  • [11] G. Calvaruso, A. Fino, Five-dimensional K-contact Lie algebras, Monatsh Math., 167 (2012).
  • [12] J. Dixmier, Sur les Repr ´ esentations unitaires des groupes de Lie nilpotentes III, Canad. J. Math., 10 (1958), 321-348.
  • [13] N. Özdemir, M. Solgun, Ş. Aktay, Quasi-Sasakian structures on 5-dimensional nilpotent Lie algebras, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019), 326-333.
  • [14] N. Özdemir, M. Solgun, Ş. Aktay, Almost contact metric structures on 5- dimensional nilpotent Lie algebras, Symmetry, 8(8) (2016), 76.
  • [15] M. P. Gong, Classification of Nilpotent Lie Algebras of Dimension 7, Ph.D. Thesis, University of Waterloo, Waterloo, Ontario, Canada, 1998.
  • [16] W. A. De Graaf, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra, 309 (2007), 640-653.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Nilüfer Özdemir 0000-0003-0507-2444

Mehmet Solgun 0000-0002-2275-7763

Şirin Aktay 0000-0003-2792-3481

Publication Date December 15, 2020
Submission Date September 25, 2020
Acceptance Date December 1, 2020
Published in Issue Year 2020 Volume: 3 Issue: 2

Cite

APA Özdemir, N., Solgun, M., & Aktay, Ş. (2020). Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras. Fundamental Journal of Mathematics and Applications, 3(2), 175-184. https://doi.org/10.33401/fujma.800222
AMA Özdemir N, Solgun M, Aktay Ş. Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras. FUJMA. December 2020;3(2):175-184. doi:10.33401/fujma.800222
Chicago Özdemir, Nilüfer, Mehmet Solgun, and Şirin Aktay. “Almost Para-Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras”. Fundamental Journal of Mathematics and Applications 3, no. 2 (December 2020): 175-84. https://doi.org/10.33401/fujma.800222.
EndNote Özdemir N, Solgun M, Aktay Ş (December 1, 2020) Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras. Fundamental Journal of Mathematics and Applications 3 2 175–184.
IEEE N. Özdemir, M. Solgun, and Ş. Aktay, “Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras”, FUJMA, vol. 3, no. 2, pp. 175–184, 2020, doi: 10.33401/fujma.800222.
ISNAD Özdemir, Nilüfer et al. “Almost Para-Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras”. Fundamental Journal of Mathematics and Applications 3/2 (December 2020), 175-184. https://doi.org/10.33401/fujma.800222.
JAMA Özdemir N, Solgun M, Aktay Ş. Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras. FUJMA. 2020;3:175–184.
MLA Özdemir, Nilüfer et al. “Almost Para-Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras”. Fundamental Journal of Mathematics and Applications, vol. 3, no. 2, 2020, pp. 175-84, doi:10.33401/fujma.800222.
Vancouver Özdemir N, Solgun M, Aktay Ş. Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras. FUJMA. 2020;3(2):175-84.

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