5 Boyutta Kuasi-para-Sasaki Yapılar Üzerine

Bu çalışmada 5 boyutlu nilpotent Lie cebirleri üzerinde kuasi-para-Sasaki yapıların varlığı incelenmiştir. Birbirine izomorf olmayan altı tane Abelyen olmayan nilpotent Lie cebri vardır. Kuasi-para-Sasaki yapıların bu Lie cebirlerinden sadece birinde olduğu gösterilmiştir. Kuasi-para-Sasaki yapılar hemen-hemen parakontak metrik yapıların sınıflandırılmasına göre G_5+G_8 sınıfına karşılık gelmektedir. 5 boyutlu nilpotent bir Lie cebri üzerinde kuasi-para-Sasaki bir yapının G_5 veya G_8 sınıfından olduğu kanıtlanmıştır.

Anahtar Kelimeler:

Hemen-hemen Parakontak Metrik Yapı, 5-boyutlu Nilpotent Lie Cebri, Kuasi-para-Sasaki Yapı

On Quasi-para-Sasakian Structures on 5-dimensions

In this study, we investigate the existence of quasi-para-Sasakian structures on five dimensional nilpotent Lie algebras. There are six non-abelian nilpotent Lie algebras. We show that quasi-para-Sasakian structures exist only on one of these algebras. Quasi-para-Sasakian structures correspond to the class G_5+G_8 in the classification of almost paracontact metric structures. We show that a quasi-para-Sasakian structure on a five dimensional nilpotent Lie algebra is either in G_5 or G_8.

Keywords:

Almost Paracontact Metric Structure, 5-dimensional Nilpotent Lie Algebra, Quasi-para-Sasakian Structure,

PDF

___

Kaneyuki, S., & Williams, F. L. (1985). Almost paracontact and parahodge structures on manifolds. Nagoya Mathematical Journal, 99, 173–187.
Zamkovoy, S. (2009). Canonical connections on paracontact manifolds. Annals of Global Analysis and Geometry, 36(37). https://doi.org/10.1007/s10455-008-9147-3
Zamkovoy, S., & Nakova, G. (2018). The decomposition of almost paracontact metric manifolds in eleven classes revisited. Journal of Geometry, 109(1), 1–23. https://doi.org/10.1007/s00022-018-0423-5
Nakova, G.,& Zamkovoy, S. (2009). Almost paracontact manifolds. arXiv:0806.3859v2 [math.DG].
Zamkovoy, S. (2018). On para-Kenmotsu manifolds. Filomat, 32(14), 4971–4980. https://doi.org/10.2298/FIL1814971Z
Özdemir, N., Solgun, M., & Aktay, ¸ S. (2020). Almost paracontact 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
Erken, I. K. (2019). Curvature properties of quasi-para-sasakian manifolds. International Electronic Journal of Geometry,, 12(2), 210–217. https://doi.org/10.36890/iejg.628085
Özdemir, N., Aktay ¸ S., & Solgun M. (2018). Almost paracontact structures obtained from G∗2(2) structures. Turkish Journal of Mathematics, 42 , 3025–3022. https://doi.org/10.3906/mat-1706-10
Dixmier, J. (1958). Sur les repr´esentations unitaires des groupes de Lie nilpotentes III. Canadian Journal of Mathematics, 10, 321–348.
Özdemir, N., Solgun, M., & Aktay, ¸ S. (2016). Almost contact metric structures on 5-dimensional nilpotent Lie algebras. Symmetry, 8, 76. https://doi.org/10.3390/sym8080076
Özdemir, N., Aktay ¸ S., & Solgun M. (2019). Quasi-Sasakian structures on 5-dimensional nilpotent Lie algebras. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 68(1), 326–333. https://doi.org/10.31801/cfsuasmas.416563
Welyczko, J. (2009). On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Results in Mathematics, 54(3), 377–387. https://doi.org/10.1007/s00025-009-0364-2 86