Non-invariant Hypersurfaces of Hyperbolic Sasakian Manifolds

Year 2021, Volume: 2 Issue: 1, 16 - 24, 09.07.2021

Toukeer Khan

Abstract

The object of this paper is to study non-invariant hypersurfaces of hyperbolic Sasakian manifolds equipped with (f,g,u,v,λ)- structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non -invariant hypersurfaces with (f,g,u,v,λ)- structure of hyperbolic Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of hyperbolic Sasakian manifolds with (f,g,u,v,λ) - structure has been traced under the condition when f is parallel.

Keywords

totally geodesic, totally umbilical, Hyperbolic Sasakian manifold

References

• Goldberg SI. Conformal transformation of Kaehler manifolds. Bulletin of American Mathematical Society. 1960. 66: 54-58.
• Goldberg SI, Yano K. Non-invariant hypersurfaces of almost contact manifolds. Journal of the Mathematical Society of Japan. 1970. 22(1): 25-34.
• Yano K, Okumura M. On (f,g,u,v,λ) – structures. Kodai Mathematical Seminar Reports. 1970. 22: 401-423.
• Blair DE, Ludden GD. Hypersurfaces in Almost Contact Manifold, Tohoku Math. J. 1969. 22: 354-362.
• Matsumoto K, Mihai I, Rosaca R. ξ-null geodesic vector fields on a LP-Sasakian manifold. J. Korean Math. Soc. 1995. 32: 17-31
• Blair DE. Contact Manifolds in Riemannian Geometry. Lecture Notes in Mathematics vol. 509. Springer-Verlag: Berlin; 1976.
• Chen BY. Geometry of submanifolds. Marcel Dekker: New York; 1973.
• Sinha BB, Sharma R. Hypersurfaces in an almost paracontact manifold. Indian J. Pure App. Math. 1978. 9: 1083-1090.
• Sarkar A, Sen M. On invariant submanifolds of trans-Sasakian manifolds. Pro. Estonian Acad. Sci. 2012. 61(1): 29-37.
• Sular S, Ozgur C. On submanifolds of Kenmotsu manifolds. Chaos, Solitons and Fractals. 2009. 42: 1990-1995.
• Khan T. On Non-invariant Hypersurfaces of a Nearly Kenmotsu Manifold. IOSR-JM. 2019. 15(6): 30-34. DOI: 10.9790/5728-1506013034.
• Prasad R. On non-invariant hypersurfaces of trans-Sasakian manifolds. Bulletin of the Calcutta Mathematical Society. 2007. 99(5): 501-510.
• Ahmed M, Khan SA, Khan T. On Non-invariant Hypersurfaces of a Nearly Hyperbolic Sasakian Manifold. International Journal of Mathematics. 2017.28(8): 1- 8. DOI: 10.1142/S0129167X17500641.
• Upadhyay MD, Dubey KK. Almost hypersurfaces contact (f,ξ,η,g)-structure. Acta Mathematica Academaiae Scientairum Hyngrical Tomus. 28 H-1053, 13.15.