HEMI-SLANT SUBMANIFOLDS OF LORENTZIAN KENMOTSU SPACE FORMS

Abstract

In this paper, we study curvature properties of hemi-slant submanifolds of Lorentzian Kenmotsu space forms. We define Lorentz Kenmotsu space forms and study their curvature properties. We give example for hemi-slant submanifold of Lorentzian Kenmotsu space forms. Finally, the curvature properties of distributions are analyzed and the conditions for Einstein are investigated.

Keywords

• Hemi-slant submanifolds
• Lorentzian Kenmotsu manifolds
• Einstein manifolds

References

1. P. Alegre, Slant submanifolds of Lorentzian Sasakian and para Sasakian manifolds, Taiwanese Journal of Mathematics, Vol.17, pp.897-910 (2013).
2. N. S. Basavarajappa, C. S. Bagewadi, D. G. Prakasha, Some results on Lorentzian beta Kenmotsu manifolds. Ann. Math. Comp.Sci. Ser, Vol.35, pp.7-14 (2008).
3. R.L. Bishop, B. ONeill, Manifolds of negative curvature, Trans. Amer. Math. Soc., Vol.145, pp.1-50 (1969).
4. S. Dirik, B.Bulut, On the geometry of contact pseudo-slant submanifolds of para beta -Kenmotsu manifolds, Bulletin of the International Mathematical Virtual Institute, Vol.14, No.1, pp.157-168 (2024).
5. S. Dirik, R. Sari, Contact Pseudo-Slant Submanifolds of Lorentzian Para Kenmotsu Manifold, Journal of Engineering Research and Applied Science, Vol.12, No.2, pp.2301-2306 (2023).
6. K. L. Duggal, Speace time manifold and contact Manifolds, Int. J. of math. and mathematical science, Vol.13, pp.545-554 (1990).
7. K. Kenmotsu, A class of almost contact Riemannian manifolds, TohokuMath. J. II Ser., Vol.24, pp.93-103 (1972).
8. M. A. Khan, K. Singh, V. A. Khan, Slant submanifolds of almost LP-contact manifold, Differential Geometry - Dynamical Systems, Vol.12, pp.102-108 (2010).

9. R. Rosca, On Lorentzian Kenmotsu manifolds, Atti Accad. Peloritana Pericolanti Cl. Aci. Fis. Mat. Natur, Vol.69, pp.15-30 (1991).
10. R. Sari, A. Vanli, Slant submanifolds of a Lorentz Kenmotsu manifold. Mediterr. J. Math.,16:129,(2019).
11. R. Sari, I. Unal, Semi-invariant submanifolds a Lorentzian Kenmotsu manifold with semi- symmetric metric connection, Bingol University Journal of Technical Science, Vol.2, No.1, pp.36-42 (2021).
12. R. Sari, S. Dirik, Generic Submanifolds of Para beta Kenmotsu Manifold, Journal of Engineering Research and Applied Science,Vol.12, No.1, pp.2291-2294 (2023).
13. T. Takahashi, Sasakian manifold with pseudo-Riemannian metric,Tohoku Math. J., Vol.21, No.2, pp.271-290 (1969).
14. I. Unal, Generic submanifolds of Lorentzian Para Kenmotsu Manifold, KMU Journal of Engineering and Natural Sciences, Vol.3, No.2, pp.79-85 (2021).
15. I. Unal, A classification of para-Kenmotsu space forms, Palestine Journal of Mathematics, 10(S.I,II), pp.197-203 (2021).