Research Article
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5 Boyutta Kuasi-para-Sasaki Yapılar Üzerine

Year 2023, Volume: 8 Issue: 1, 75 - 86, 21.07.2023
https://doi.org/10.33484/sinopfbd.1295803

Abstract

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.

Project Number

22 ADP 011

References

  • 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

On Quasi-para-Sasakian Structures on 5-dimensions

Year 2023, Volume: 8 Issue: 1, 75 - 86, 21.07.2023
https://doi.org/10.33484/sinopfbd.1295803

Abstract

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.

Supporting Institution

Eskişehir Technical University

Project Number

22 ADP 011

References

  • 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
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Şirin Aktay 0000-0003-2792-3481

Ümmü Kocabaş 0000-0003-0946-5544

Project Number 22 ADP 011
Early Pub Date July 20, 2023
Publication Date July 21, 2023
Submission Date May 11, 2023
Published in Issue Year 2023 Volume: 8 Issue: 1

Cite

APA Aktay, Ş., & Kocabaş, Ü. (2023). On Quasi-para-Sasakian Structures on 5-dimensions. Sinop Üniversitesi Fen Bilimleri Dergisi, 8(1), 75-86. https://doi.org/10.33484/sinopfbd.1295803