# LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM WITH A SYMMETRIC METRIC CONNECTION OF TYPE (ℓ, m)

Jin, Dae Ho

• Published : 2016.07.31
• 17 2

#### Abstract

We define a new connection on a semi-Riemannian manifold. Its notion contains two well known notions; (1) semi-symmetric connection and (2) quarter-symmetric connection. In this paper, we study the geometry of lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (${\ell}$, m).

#### Keywords

symmetric connection of type (${\ell}$, m);metric connection;lightlike hypersurface

#### References

1. P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian space form, Israel J. Math. 141 (2004), 157-183. https://doi.org/10.1007/BF02772217
2. C. Atindogbe and K. L. Duggal, Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math. 11 (2004), no. 4, 421-442.
3. C. Calin, Contributions to geometry of CR-submanifold, Thesis, University of Iasi, Romania, 1998.
4. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
5. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
6. K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
7. S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.) 29 (1975), no. 3, 249-254.
8. H. A. Hayden, Subspace of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.
9. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold, Indian J. Pure Appl. Math. 41 (2010), no. 4, 569-581. https://doi.org/10.1007/s13226-010-0032-y
10. D. H. Jin, Half lightlike submanifold of an indefinite generalized Sasakian space form with a quarter-symmetric metric connection, Internat. Math. Forum 10 (2015), no. 3, 127-142. https://doi.org/10.12988/imf.2015.517
11. D. Kamilya and U. C. De, Some properties of a Ricci quarter-symmetric metric connection in a Riemannian manifold, Indian J. Pure Appl. Math. 26 (1995), no. 1, 29-34.
12. R. S. Mishra and S. N. Pandey, On quarter symmetric metric F-connections, Tensor (N.S.) 34 (1980), no. 1, 1-7.
13. J. Nikic and N. Pusic, A remakable class of natural metric quarter-symmetric connection on a hyperbolic Kaehler space, Conference "Applied Differential Geometry: General Relativity"-Workshop "Global Analysis, Differential Geometry, Lie Algebras", 96-101, BSG Proc., 11, Geom. Balkan Press, Bucharest, 2004.
14. J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187-193.
15. N. Pusic, On quarter-symmetric metric connections on a hyperbolic Kaehlerian space, Publ. Inst. Math. (Beograd) (N.S.) 73(87) (2003), 73-80. https://doi.org/10.2298/PIM0373073P
16. S. C. Rastogi, On quarter-symmetric metric connections, C. R. Acad Sci. Bulgare Sci. 31 (1978), no. 7, 811-814.
17. S. C. Rastogi, On quarter-symmetric metric connections, Tensor (N.S.) 44 (1987), no. 2, 133-141.
18. K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.
19. K. Yano and T. Imai, Quarter-symmetric metric connection and their curvature tensors, Tensor (N.S.) 38 (1982), 13-18.