EN
A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms
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 $\sigma=0$.
Keywords
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
October 15, 2021
Submission Date
November 18, 2020
Acceptance Date
September 20, 2021
Published in Issue
Year 2021 Volume: 9 Number: 2
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. https://izlik.org/JA68JC53EH
AMA
1.Atçeken M, Uygun P. A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms. Konuralp J. Math. 2021;9(2):310-315. https://izlik.org/JA68JC53EH
Chicago
Atçeken, Mehmet, and Pakize Uygun. 2021. “A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms”. Konuralp Journal of Mathematics 9 (2): 310-15. https://izlik.org/JA68JC53EH.
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
[1]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, Oct. 2021, [Online]. Available: https://izlik.org/JA68JC53EH
ISNAD
Atçeken, Mehmet - Uygun, Pakize. “A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms”. Konuralp Journal of Mathematics 9/2 (October 1, 2021): 310-315. https://izlik.org/JA68JC53EH.
JAMA
1.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, Oct. 2021, pp. 310-5, https://izlik.org/JA68JC53EH.
Vancouver
1.Mehmet Atçeken, Pakize Uygun. A Classification of Submanifolds of $(\kappa,\mu)$-Paracontact Metric Space Forms. Konuralp J. Math. [Internet]. 2021 Oct. 1;9(2):310-5. Available from: https://izlik.org/JA68JC53EH
