Examples of Almost Para-Contact Metric Structures on 5-dimensions

Year 2022, , 89 - 97, 01.06.2022

Ümmü Kocabaş , Şirin Aktay

https://doi.org/10.33401/fujma.1049969

Cited By: 1

Abstract

In this study, the classes of several almost paracontact metric structures on 5 dimensional nilpotent Lie algebras are determined. It is also shown that there are no $\eta-$ Einstein structures on 5 dimensional nilpotent Lie algebras.

Keywords

Almost paracontact metric structure, \eta-Einstein manifold, 5-dimensional nilpotent Lie algebra, Nilpotent Lie algebra

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. Global Anal. Geom., 36 (2009), 37-60, https://doi.org/10.1007/s10455-008-9147-3.
• [3] S. Zamkovoy, G. Nakova, The decomposition of almost paracontact metric manifolds in eleven classes revisited, J. Geom., 109 (1), (2018), 1-23.
• [4] G. Nakova, S. Zamkovoy, Almost paracontact manifolds, (2009), arXiv:0806.3859v2 [math.DG].
• [5] S. Zamkovoy, On para-Kenmotsu manifolds, Filomat, 32 (14) (2018), 4971-4980, https://doi.org/10.2298/FIL1814971Z.
• [6] N. Özdemir, Ş. Aktay, M. Solgun, Almost paracontact structures obtained from G 2(2) structures, Turk. J. Math., 42 (2018), 3025-3022, https://doi.org/10.3906/mat-1706-10.
• [7] J. Dixmier, Sur les repr ´ esentations unitaires des groupes de Lie nilpotentes III, Canad. J. Math., 10 (1958), 321-348.
• [8] N. Özdemir, M. Solgun, Ş. Aktay, Almost paracontact metric structures on 5-dimensional nilpotent Lie algebras, Fundam. J. Math. Appl., 3 (2), (2020), 175-184, https://doi.org/10.33401/fujma.800222.