SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2023 / Volume: 15 Issue: 2

Pseudoparallel Invariant Submanifolds of a Para-Sasakian Manifold

Tuğba Mert(SIVAS CUMHURIYET UNIVERSITY)0000-0001-8258-8298
Mehmet Atçeken(AKSARAY UNIVERSITY)0000-0002-1242-4359
Pages
—
Publication Date
2023-12-31
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The necessary and sufficient conditions for an invariant submanifold to be totally geodesic under some conditions have been given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, invariant submanifolds of a para-Sasakian manifold have been studied.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:The necessary and sufficient conditions for an invariant submanifold to be totally geodesic under some conditions have been given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Para-Sasakian manifold · pseudoparallel · Ricci-generalized pseudoparallel and 2-pseudoparallel submanifolds

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.

🔖

Cite This Article

Mert, T., Atçeken, M. (2023). Pseudoparallel Invariant Submanifolds of a Para-Sasakian Manifold. Turkish Journal of Mathematics and Computer Science, Volume: 15 Issue: 2. https://doi.org/10.47000/tjmcs.1124668

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. 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.
  2. Asperti, A.C., Lobos, G.A., Mercuri, F., Pseudoparallel immersion in space forms, 10th School on Differential Geometry Mat. Contemp, 17(1998), 59–70.
  3. Atçeken, M., Yıldırım, Ü., Dirik, S., Semiparallel submanifolds of a normal paracontact metric manifold, Hacettepe J. of Math. and Stat., 48(2019), 501–509.
  4. Bahadır, O., Lorentzian para-Sasakian manifold with quarter-symmetric non-metricconnection, Journal of Dynamical Systems and Geometric Theories, 14(1)(2016), 17–33.
  5. Bahadır, O., P-Sasakian manifold with quarter-symmetric non-metric connection, Universal Journal of Applied Mathematics, 6(4)(2018), 123–133.
  6. Guojing, Z., Jianguo, W., Invariant submanifolds and modes of non-linear autonomous system, Appl. Math. Mech., 19(1998), 587–693.
  7. 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.
  8. 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.
  9. Kobayashi, M., Semi invariant submanifolds of a certain class of almost contact metric manifolds, Tensor (N.S), 43(1986), 28–36.
  10. Kon, M., Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep., 27(1973), 330–336.
  11. Montano, B.C., Terlizzi, L.D., Tripathi, M.M., Invariant submanifolds of contact (k, η) −manifolds, Glasgow Math. J., 50(2008), 499–507.
  12. Sarkar, A., Sen, M., On invariant submanifolds trans-Sasakian manifolds, Proc. Estonian Acad. Sci., 61(2012), 29–37.
  13. Shukla, S.S., On ϕ−Symmetric para-Sasakian manifolds, Int. Journal of Math. Analysis, 16(2010), 761–769.
  14. 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.
  15. Sular, S., Kenmotsu Manifolds and Some of Their Submanifolds, Ph.D. Thesis, Balikesir University, Institute of Science and Technology, 2009.
  16. Sular, S., Özgür, C., Murathan, C., Pseudoparallel anti-invariant submanifolds of Kenmotsu manifolds, Hacettepe J. of Math. and Stat., 39(2010), 535–543.
  17. Venkatesha, Naik, D.M., Certain results on K-paracontact and para-Sasakian Manifolds, J. Geom., 108(2017), 939–952.
  18. Atçeken, M., Yıldırım, Ü., Dirik, S., Semiparallel submanifolds of a normal paracontact metric manifold, Hacettepe J. of Math. and Stat., 48(2019), 501–509.