Some Characterizations Invariant Submanifolds of A (κ,μ)-Para Contact Space
Keywords:
κ,μ- Paracontact metric manifold, Invariant submanifold, semiparallel submanifold, 2-semiparallel submanifold
Abstract
The aim of this present paper is to study certain conditions for an invariant submanifold of a κ,μ- paracontact space. We classify paracontact space form satisfying the curvature conditions 0. Recently, we reach at these conditions are equivalent to 0.
References
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[16] Prakasha, D.G., Mirji, K., "On (κ,μ)-Paracontact Metric Manifolds", Gen. Math. Notes. 25(2) (2014): 68-77.
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[19] Uygun, P., Atçeken, M., Dirik, S., "Some curvature results on Kenmotsu metric spaces", Bull. Int. Math. Virtual Inst, 12(2) (2022): 243-251.
[20] Uygun, P., Atçeken, M., Dirik, S., "On Kenmotsu metric spaces satisfying some conditions on the W_1-curvature tensor", Filomat, 36(5), (2022): 1603-1613.
[21] Venkatesha, V., Basavarajappa, S., "Invariant Submanifolds of LP-Sasakian Manifolds", Khayyam J. Math. 6(1) (2020): 16-26.
[22] Zamkovoy, S., "Canonical Connections on Paracontact Manifolds", Annals of Global Analysis and Geometry. 36(1) (2009): 37-60.
[23] Zamkovoy, S., "Canonical Connections on Paracontact Manifolds", Annals of Global Analysis and Geometry. 36(1) (2009): 68-77.
[2] Atçeken, M., Mert, T.,"Characterizations for totally geodesic submanifolds of a K-paracontact manifolds", Aims Mathematics. 6(7)(2021): 7320-7332.
[3] Atçeken, M., Uygun, P., "Characterizations for totally geodesic submanifolds of (κ,μ)-Paracontact Metric Manifolds", Korean J. Math. 28(3)(2020): 555-571.
[4] Atçeken, M., Yildirim, Ü., Dirik, S., "Semi-Parallel Submanifolds of a Normal Paracontact Metric Manifold", Hacet. J. Math. Stat. Volume 48(2)(2019): 501-509, 10.15672/HJMS.2017.
[5] Bejancu, A., Papaghuic, N., "Semi-Invariant submanifolds of a Sasakian manifold", An. Ştint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 27 (1981): 163-170.
[6] Bejancu, A., Papaghuic, N., "Semi-Invariant submanifolds of a Sasakian space form", Collog. Math. 48 (1984): 77-88.
[7] De, U.C., Samui, S., "On Some Classes of Invariant Submanifolds of Lorentzian Para-Sasakian Manifolds", Tamkang J. Math. 47(2) (2016): 207-220.
[8] Hu, C., Wang, V., "A Note an Invariant Submanifolds of Trans-Sasakian Manifolds", Int. Electron J. Geom. 9(2)(2016): 27-35.
[9] Kaneyuki, S., Williams, F.L., "Almost Paracontact and Parahodge Structures on Manifolds", Nayoga Mathematical Journal. Vol. 99 (1985): 173-187.
[10] Kon, M., "Invariant submanifoldsof normal contact metric manifolds", Kodai Math. Sem. Rep., 25(1973): 330-336.
[11] Kowalezyk, D., "On Some Subclass of Semisymmetric Manifolds", Soochow J. Math. 27 (2001): 445-461.
[12] Lee, J.E., "Slant curves and Frenet curves in 3-dimensional para-Sasakian manifolds", Balkan Journal of Geometry and ıts Applications 26(1)(2021): 21-33.
[13] Makhal, S., De, U.C., "On Pseudo-Symmetric Curvature Conditions of Generalized (κ,μ)-Paracontact Metric Manifolds", Konuralp J. of Mathematics. 5(2) (2017): 239-247.
[14] Montano, B.C., Erken, F.K., Murathan, C., "Nullity Conditions in Paracontact Geometry", Differential Geometry and Its Applications. 30(6) (2012): 665-693.
[15] Pokhariyal, G.P., "Relativistic significance of curvature tensors", Internat. J. Math. Sci., 5(1) (1982): 133-139.
[16] Prakasha, D.G., Mirji, K., "On (κ,μ)-Paracontact Metric Manifolds", Gen. Math. Notes. 25(2) (2014): 68-77.
[20] Prasad, B., "A pseudo projective curvature tensor on a Riemannian manifold", Bull. Caulcutta Math. Soc., 94(3) (2002): 163-166.
[18] Rovenski, V., "The Einstein-Hilbert type action on almost multi-product manifolds", Balkan Journal of Geometry and ıts Applications 26(1)(2021): 81-92.
[19] Uygun, P., Atçeken, M., Dirik, S., "Some curvature results on Kenmotsu metric spaces", Bull. Int. Math. Virtual Inst, 12(2) (2022): 243-251.
[20] Uygun, P., Atçeken, M., Dirik, S., "On Kenmotsu metric spaces satisfying some conditions on the W_1-curvature tensor", Filomat, 36(5), (2022): 1603-1613.
[21] Venkatesha, V., Basavarajappa, S., "Invariant Submanifolds of LP-Sasakian Manifolds", Khayyam J. Math. 6(1) (2020): 16-26.
[22] Zamkovoy, S., "Canonical Connections on Paracontact Manifolds", Annals of Global Analysis and Geometry. 36(1) (2009): 37-60.
[23] Zamkovoy, S., "Canonical Connections on Paracontact Manifolds", Annals of Global Analysis and Geometry. 36(1) (2009): 68-77.
Published
2022-06-30
How to Cite
Uygun, P., Dirik, S., Atceken, M., & Mert, T. (2022). Some Characterizations Invariant Submanifolds of A (κ,μ)-Para Contact Space. Journal of Engineering Research and Applied Science, 11(1), 1967-1972. Retrieved from http://www.journaleras.com/index.php/jeras/article/view/274
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