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Year 2021, Volume: 9 Issue: 2, 310 - 315, 15.10.2021

Abstract

References

  • Arslan, K.; Lumiste, U.; Murathan, C.; Özgür, C.; 2-Semiparallel Surfaces in Space Forms 1. Two Particular Cases. Proc. Estonian Acad. Sci. Phys. Math. 49(3), 139-148, 2000.
  • Atceken, M.; Yildirim, Ü.; Dirik, S. Semiparallel Submanifolds of a Normal Paracontact Metric Manifold. Hacet. J. Math. Stat. Volume 48 (2) (2019), 501 509.
  • Blair, D. E.; Koufogiorgos, T.; Papatoniou, B. J. Contact Metric Manifolds Satisfying a Nullity Conditions. Israel J. Math. 91(1995). 189-214.
  • Cappletti-Montano,; Küpeli, B.; Erkan, I.; Murathan, C. Nullity Conditions in Paracontact Geometry. Di®. Geom. Appl. 30(2012). 665-693.
  • Koneyuki, S.; Williams, F. I. Almost Paracontact and Paragodge Structures on Manifolds. Nayoga Maht. J. 99(1985, 173-187.)
  • Özgür, C.; Gürler, F.; Murathan, C. On Semiparallel Anti Invariant Submanifolds of Generalized Sasakian Space forms, Turk J. Math. 38, 796-802, 2014.
  • Zamkovay, S. Canonical Connection on Paracontact Manifolds. Ann. Global Anal. Geom. 36(2009) 37-60.
  • Hui, S. K., Uddin, S and Mandal, P. Submanifolds of generalized (·; ¹)-space forms. Period Math Hung 77, 329-339(2018). https://doi.org//10.1007/S10998-018-0248-x.
  • Hui, S. K., Uddin, S., Alkhaldi, A. H and Mandal, P. Invariant submanifolds of generalized Sasakian-space-forms. International Journal of Geometric Methods in Modern Physics. Vol. 15(2018)1850149(21 pages)https://doi.org/10.1142/50219887818501499.

A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms

Year 2021, Volume: 9 Issue: 2, 310 - 315, 15.10.2021

Abstract

The aim of this paper is to study the invariant submanifolds of a $(\kappa, \mu)$-paracontact metric space form. We characterize $(\kappa,\mu)$-paracontact metric space form satisfying the curvature conditions $\nabla\sigma$=0, $R\cdot{\sigma}=0$, $R\cdot{\nabla\sigma}=0$ and $\widetilde{C}\cdot\sigma=0$. Finally, we see that these conditions are equivalent to $\sigma=0$.

References

  • Arslan, K.; Lumiste, U.; Murathan, C.; Özgür, C.; 2-Semiparallel Surfaces in Space Forms 1. Two Particular Cases. Proc. Estonian Acad. Sci. Phys. Math. 49(3), 139-148, 2000.
  • Atceken, M.; Yildirim, Ü.; Dirik, S. Semiparallel Submanifolds of a Normal Paracontact Metric Manifold. Hacet. J. Math. Stat. Volume 48 (2) (2019), 501 509.
  • Blair, D. E.; Koufogiorgos, T.; Papatoniou, B. J. Contact Metric Manifolds Satisfying a Nullity Conditions. Israel J. Math. 91(1995). 189-214.
  • Cappletti-Montano,; Küpeli, B.; Erkan, I.; Murathan, C. Nullity Conditions in Paracontact Geometry. Di®. Geom. Appl. 30(2012). 665-693.
  • Koneyuki, S.; Williams, F. I. Almost Paracontact and Paragodge Structures on Manifolds. Nayoga Maht. J. 99(1985, 173-187.)
  • Özgür, C.; Gürler, F.; Murathan, C. On Semiparallel Anti Invariant Submanifolds of Generalized Sasakian Space forms, Turk J. Math. 38, 796-802, 2014.
  • Zamkovay, S. Canonical Connection on Paracontact Manifolds. Ann. Global Anal. Geom. 36(2009) 37-60.
  • Hui, S. K., Uddin, S and Mandal, P. Submanifolds of generalized (·; ¹)-space forms. Period Math Hung 77, 329-339(2018). https://doi.org//10.1007/S10998-018-0248-x.
  • Hui, S. K., Uddin, S., Alkhaldi, A. H and Mandal, P. Invariant submanifolds of generalized Sasakian-space-forms. International Journal of Geometric Methods in Modern Physics. Vol. 15(2018)1850149(21 pages)https://doi.org/10.1142/50219887818501499.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Atçeken

Pakize Uygun

Publication Date October 15, 2021
Submission Date November 18, 2020
Acceptance Date September 20, 2021
Published in Issue Year 2021 Volume: 9 Issue: 2

Cite

APA Atçeken, M., & Uygun, P. (2021). A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms. Konuralp Journal of Mathematics, 9(2), 310-315.
AMA Atçeken M, Uygun P. A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms. Konuralp J. Math. October 2021;9(2):310-315.
Chicago Atçeken, Mehmet, and Pakize Uygun. “A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms”. Konuralp Journal of Mathematics 9, no. 2 (October 2021): 310-15.
EndNote Atçeken M, Uygun P (October 1, 2021) A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms. Konuralp Journal of Mathematics 9 2 310–315.
IEEE M. Atçeken and P. Uygun, “A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms”, Konuralp J. Math., vol. 9, no. 2, pp. 310–315, 2021.
ISNAD Atçeken, Mehmet - Uygun, Pakize. “A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms”. Konuralp Journal of Mathematics 9/2 (October 2021), 310-315.
JAMA Atçeken M, Uygun P. A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms. Konuralp J. Math. 2021;9:310–315.
MLA Atçeken, Mehmet and Pakize Uygun. “A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms”. Konuralp Journal of Mathematics, vol. 9, no. 2, 2021, pp. 310-5.
Vancouver Atçeken M, Uygun P. A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms. Konuralp J. Math. 2021;9(2):310-5.
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