Year 2021,
Volume: 9 Issue: 2, 310 - 315, 15.10.2021
Mehmet Atçeken
,
Pakize Uygun
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
Mehmet Atçeken
,
Pakize Uygun
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.