Research Article
Year 2023,
Volume: 15 Issue: 2, 382 - 390, 31.12.2023
Abstract
In this paper, invariant submanifolds of a para-Sasakian manifold have been studied. Some special
submanifolds such as pseudoparallel, 2-pseudoparallel, Ricci generalized pseudoparallel, and 2-Ricci generalized pseudoparallel submanifolds of a para-Sasakian manifold have been considered. The necessary and sufficient conditions for an invariant submanifold to be totally geodesic under some conditions have been given.
Keywords
Para-Sasakian manifold pseudoparallel Ricci-generalized pseudoparallel and 2-pseudoparallel submanifolds
References
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- Bahadır, O., P-Sasakian manifold with quarter-symmetric non-metric connection, Universal Journal of Applied Mathematics, 6(4)(2018), 123–133.
- Guojing, Z., Jianguo, W., Invariant submanifolds and modes of non-linear autonomous system, Appl. Math. Mech., 19(1998), 587–693.
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- Montano, B.C., Terlizzi, L.D., Tripathi, M.M., Invariant submanifolds of contact (k, η) −manifolds, Glasgow Math. J., 50(2008), 499–507.
- Sarkar, A., Sen, M., On invariant submanifolds trans-Sasakian manifolds, Proc. Estonian Acad. Sci., 61(2012), 29–37.
- Shukla, S.S., On ϕ−Symmetric para-Sasakian manifolds, Int. Journal of Math. Analysis, 16(2010), 761–769.
- Siddesha, M., Bagewadi, C.S., On some clases an ınvariant submanifolds of (k, μ) −contact manifold, J. of inforatics and mathematical sciences, 9(1)(2017), 13–26.
- Sular, S., Kenmotsu Manifolds and Some of Their Submanifolds, Ph.D. Thesis, Balikesir University, Institute of Science and Technology, 2009.
- Sular, S., Özgür, C., Murathan, C., Pseudoparallel anti-invariant submanifolds of Kenmotsu manifolds, Hacettepe J. of Math. and Stat., 39(2010), 535–543.
- Venkatesha, Naik, D.M., Certain results on K-paracontact and para-Sasakian Manifolds, J. Geom., 108(2017), 939–952.
Year 2023,
Volume: 15 Issue: 2, 382 - 390, 31.12.2023
Abstract
References
- Arslan, K., Lumiste, U., Murathan, C., Özgür, C., 2-semiparallel surfaces in space forms, Two particular cases, Proc. Estonian Acad. Sci. Phys. Math., 49(3)(2000), 139–148.
- Asperti, A.C., Lobos, G.A., Mercuri, F., Pseudoparallel immersion in space forms, 10th School on Differential Geometry Mat. Contemp, 17(1998), 59–70.
- Atçeken, M., Yıldırım, Ü ., Dirik, S., Semiparallel submanifolds of a normal paracontact metric manifold, Hacettepe J. of Math. and Stat., 48(2019), 501–509.
- Bahadır, O., Lorentzian para-Sasakian manifold with quarter-symmetric non-metricconnection, Journal of Dynamical Systems and Geometric Theories, 14(1)(2016), 17–33.
- Bahadır, O., P-Sasakian manifold with quarter-symmetric non-metric connection, Universal Journal of Applied Mathematics, 6(4)(2018), 123–133.
- Guojing, Z., Jianguo, W., Invariant submanifolds and modes of non-linear autonomous system, Appl. Math. Mech., 19(1998), 587–693.
- Hui, S.K., Mishra, V.N., Pal, T.,Vandana, Some classes of invariant submanifolds of (LCS )n −manifolds, Italian J. of Pure and Appl. Math., 39(2018, 359–372.
- Hui, S.K, Uddin, S., Alkhaldi, A.H., Mandal, P., Invariant submanifolds of generalized Sasakian-space forms, International Journal of Geometric Methods in Modern Physics, 15(2018), 1–21.
- Kobayashi, M., Semi invariant submanifolds of a certain class of almost contact metric manifolds, Tensor (N.S), 43(1986), 28–36.
- Kon, M., Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep., 27(1973), 330–336.
- Montano, B.C., Terlizzi, L.D., Tripathi, M.M., Invariant submanifolds of contact (k, η) −manifolds, Glasgow Math. J., 50(2008), 499–507.
- Sarkar, A., Sen, M., On invariant submanifolds trans-Sasakian manifolds, Proc. Estonian Acad. Sci., 61(2012), 29–37.
- Shukla, S.S., On ϕ−Symmetric para-Sasakian manifolds, Int. Journal of Math. Analysis, 16(2010), 761–769.
- Siddesha, M., Bagewadi, C.S., On some clases an ınvariant submanifolds of (k, μ) −contact manifold, J. of inforatics and mathematical sciences, 9(1)(2017), 13–26.
- Sular, S., Kenmotsu Manifolds and Some of Their Submanifolds, Ph.D. Thesis, Balikesir University, Institute of Science and Technology, 2009.
- Sular, S., Özgür, C., Murathan, C., Pseudoparallel anti-invariant submanifolds of Kenmotsu manifolds, Hacettepe J. of Math. and Stat., 39(2010), 535–543.
- Venkatesha, Naik, D.M., Certain results on K-paracontact and para-Sasakian Manifolds, J. Geom., 108(2017), 939–952.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 31, 2023 |
| Published in Issue | Year 2023 Volume: 15 Issue: 2 |