Semi-Invariant Submanifolds A Lorentzian Kenmotsu Manifold With Semi-Symmetric Metric Connection

Year 2021, Volume: 2 Issue: 1, 36 - 42, 09.07.2021

Ramazan Sarı İnan Ünal

Abstract

In this paper, semi-invariant submanifolds of a lorentzian Kenmotsu manifold endowed with a semi-symmetric metric connection are studied. Necessary and sufficient conditions are given on a submanifold of a lorentzian Kenmotsu manifold to be semi-invarinat submanifold with the semi-symmetric metric connection. Moreover, the parallel conditions of the distribution on semi-invariant submanifolds of a lorentzian Kenmotsu manifold with the semi-symmetric metric.

Keywords

Lorentzian Kenmotsu manifold, semi invariant submanifold, semi symmetric metric connection

References

• Bishop RL, O'Neill B. Manifolds of negative curvature. Trans. Amer. Math. Soc.1969. 145: 1-50.
• Duggal KL. Speace time manifold and contact Manifolds. Int. J. of math. And mathematical science. 1990. 13: 545-554.
• Friedmann A, Schouten JA. Uber die Geometric der halbsymmetrischen Ubertragung. Math. Z. 1924. 21: 211-223.
• Kenmotsu K. A class of almost contact Riemannian manifolds. TohokuMath. J. II Ser. 1972. 24: 93-103.
• Kobayashi M. Semi-invariant submanifolds of a certain class of almost contact manifolds. Tensor N. S. 1986. 43: 28-36.
• Nirmala SA, Mangala RC. A semi-symmetric non-metric connection on Riemannian manifold. Indiana J. Pure Appl. Math. 1992. 23: 399-40.
• Roşca R. On Lorentzian Kenmotsu manifolds. Atti Accad. Peloritana Pericolanti, Cl. Sci. 1991. 69: 15-30.
• Sarı R, Vanlı A. Slant submanifolds of a Lorentz Kenmotsu manifold. Mediterr. J. Math. 2019. 16:129.
• Sarı R. Some Properties Curvture of Lorentzian Kenmotsu Manifolds. Applied Mathematics and Nonlinear Sciences. 2020. 5(1): 283–292.
• Sinha BB, Srivastava AK. Semi-invariant submanifolds of a Kenmotsu manifold with constant φ-holomorphic sectional curvature. Indian J. pure appl. Math. 1992. 23(11): 783-789.
• Takahashi T. Sasakian manifold with pseudo-Riemannian metric. Tohoku Math. J. 1969. 21(2): 271-290.
• Turgut Vanli A, Sari R. On semi invariant submanifolds of generalized Kenmotsu manifolds with semi symmetric metric connection. Acta Universitatis Apulensis. 2015. 43: 79-92.
• Yano K. On semi-symmetric metric connection. Rev. Roumaine Math. Pures Appl. 1970. 15: 1579-1586.