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

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. [1] S. Kaneyuki, F. L. Williams, Almost paracontact and Parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
2. [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. [3] G. Nakova, S. Zamkovoy, Almost paracontact manifolds, arXiv:0806.3859v2.
4. [4] S. Zamkovoy, On Para-Kenmotsu manifolds, arXiv:1711.03008v1.
5. [5] G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2) (2011), 697-718.
6. [6] G. Calvaruso, A. Perrone, Five-dimensional paracontact Lie algebras, Differ. Geom. Appl., 45 (2016), 115-129.
7. [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. [8] A. Zaitov, D. Ilxomovich Jumaev, Hyperspaces of superparacompact spaces and continuous maps, Univers. J. Math. Appl. 2(2) (2019), 65-69.

9. [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.
10. [11] G. Calvaruso, A. Fino, Five-dimensional K-contact Lie algebras, Monatsh Math., 167 (2012).
11. [12] J. Dixmier, Sur les Repr ´ esentations unitaires des groupes de Lie nilpotentes III, Canad. J. Math., 10 (1958), 321-348.
12. [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.
13. [14] N. Özdemir, M. Solgun, Ş. Aktay, Almost contact metric structures on 5- dimensional nilpotent Lie algebras, Symmetry, 8(8) (2016), 76.
14. [15] M. P. Gong, Classification of Nilpotent Lie Algebras of Dimension 7, Ph.D. Thesis, University of Waterloo, Waterloo, Ontario, Canada, 1998.
15. [16] W. A. De Graaf, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra, 309 (2007), 640-653.