SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2016 / Volume: 9 Issue: 2

A Note on Invariant Submanifolds of Trans-Sasakian Manifolds

Chaogui Hu
Yaning Wang
Pages
—
Publication Date
2016-10-30
🏛️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)

In addition, we construct an

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The object of this paper is to obtain some necessary and sufficient conditions for an invariant  submanifold of a trans-Sasakian manifold to be totally geodesic.
📊
Key Findings & Data:The object of this paper is to obtain some necessary and sufficient conditions for an invariant  submanifold of a trans-Sasakian manifold to be totally geodesic.
💡
Conclusion & Impact:In addition, we construct an
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:invariant submanifold · trans-Sasakian manifold · totally geodesic

Abstract

The object of this paper is to obtain some necessary and sufficient conditions for an invariant  submanifold of a trans-Sasakian manifold to be totally geodesic. In addition, we construct an

🔖

Cite This Article

Hu, C., Wang, Y. (2016). A Note on Invariant Submanifolds of Trans-Sasakian Manifolds. International Electronic Journal of Geometry, Volume: 9 Issue: 2. https://doi.org/10.36890/iejg.584576

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Arslan, K., Lumiste, U., Murathn, C. and Özgür, C., 2-semiparallel surfaces in space forms, I: two particular cases, Proc. Est. Acad. Sci. Phys. Math. 49 (2000), no. 3, 139–148.
  2. Asperti, A. C., Lobos, G. A. and Mercuri, F., Pseudo-parallel immersions in space forms, Mat. Contemp. 17 (1999), 59–70.
  3. Blair, D. E. and Oubina, J. A., Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mat. 34 (1990), no. 1, 199–207.
  4. Chinea, D. and Prestelo, P. S., Invariant submanifolds of a trans-Sasakian manifold, Publ. Math. Debrecen 38 (1991), no, 1-2, 103–109.
  5. De, A., Totally geodesic submanifolds of a trans-Sasakian manifold, Proc. Est. Acad. Sci. 62 (2013), no. 4, 249–257.
  6. De, U. C. and Majhi, P., On invariant submanifolds of Kenmotsu manifolds, J. Geom. 106 (2015), no. 1, 109–122.
  7. Deprez, J., Semi-parallel surfaces in Euclidean space, J. Geom. 25 (1985), no. 2, 192–200.
  8. Deshmukh, S. and Tripathi, M. M., A note on trans-Sasakian manifolds, Math. Slovaca 63 (2013), no. 6, 1361–1370.
  9. Gray, A. and Hervella, L. M., The sixteen classes of almost Heritian manifolds and their linear invariants, Ann. Mat. Pura Appl. 123 (1980), no. 1, 35–58.
  10. Kobayashi, M., Semi-invariant submanifolds of a certain class of almost contact metric manifolds, Tensor (N.S.) 43 (1986), no. 1, 28–36.
  11. Kon, M., Invariant submanifols of normal contact metric manifolds, Kodai Math. Sem. Rep. 25 (1973), no. 3, 330–336.
  12. Kowalczyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math. 27 (2001), no. 4, 445–462.
  13. Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie 39 (1996), no. 1-4, 183–198.
  14. Mangione, V., Totally geodesic submanifolds of a Kenmotsu space form, Math. Reports 7 (2005), no. 4, 315–324.
  15. Murathan, C., Arslan, K. and Ezentas, E., Ricci generalized pseudo-symmetric immersions, Differ. Geom. Appl. 99–108, Matfyzpress, Prague, 2005.
  16. Oubina, J. A., New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187–193.
  17. Prasad, R. and Srivastava, V., Some results on trans-Sasakian manifofold, Mat. Vesnik. 65 (2013), no. 3, 346–352.
  18. Sarkar, A. and Sen, M., On invariant submanifolds of trans-Sasakian manifolds, Proc. Est. Acad. Sci. 61 (2012), no. 1, 29–37.
  19. Sular, S. and Özgür, C., On some submanifolds of Kenmotsu manifolds, Chaos Soliton Fract. 42 (2009), no. 4, 1990–1995.
  20. Vanli, A. T. and Sari, R., Invariant submanifolds of trans-Sasakian manifolds, Differ. Geom. Dyn. Syst. 12 (2010), 277–288.
  21. Verstraelen, L., Comments on pseudosymmetry in the sense of Ryszard Deszcz, Geometry and Topology of submanifolds, 6 (1994), no. 1,199–209.