## Journal of Applied Mathematics

### Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

Dae Ho Jin

#### Abstract

We study lightlike hypersurfaces $M$ of an indefinite generalized Sasakian space form $\stackrel{-}{M}({f}_{1},{f}_{2},{f}_{3})$, with indefinite trans-Sasakian structure of type $(\alpha ,\beta )$, subject to the condition that the structure vector field of $\stackrel{-}{M}$ is tangent to $M$. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type $(\alpha ,\beta )$. Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.

#### Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 259146, 9 pages.

Dates
First available in Project Euclid: 15 April 2015

https://projecteuclid.org/euclid.jam/1429105056

Digital Object Identifier
doi:10.1155/2015/259146

Mathematical Reviews number (MathSciNet)
MR3335445

Zentralblatt MATH identifier
1346.53021

#### Citation

Jin, Dae Ho. Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms. J. Appl. Math. 2015 (2015), Article ID 259146, 9 pages. doi:10.1155/2015/259146. https://projecteuclid.org/euclid.jam/1429105056

#### References

• J. A. Oubiña, “New classes of almost contact metric structures,” Publicationes Mathematicae Debrecen, vol. 32, no. 3-4, pp. 187–193, 1985.
• P. Alegre, D. E. Blair, and A. Carriazo, “Generalized Sasakian-space-forms,” Israel Journal of Mathematics, vol. 141, pp. 157–183, 2004.
• D. H. Jin, “Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold,” Indian Journal of Pure and Applied Mathematics, vol. 41, no. 4, pp. 569–581, 2010.
• D. H. Jin, “The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold,” Balkan Journal of Geometry and its Applications, vol. 17, no. 1, pp. 49–57, 2012.
• D. H. Jin, “Geometry of lightlike hypersurfaces of an indefinite cosymplectic manifold,” Communications of the Korean Mathematical Society, vol. 27, no. 1, pp. 185–195, 2012.
• K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, vol. 364, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
• K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of semi-Riemannian manifolds, World Scientific, River Edge, NJ, USA, 2007.
• C. Călin, Contributions to geometry of CR-submanifold [M.S. thesis], University of Iasi, Iasi, Romania, 1998.
• G. de Rham, “Sur la réductibilité d'un espace de Riemann,” Commentarii Mathematici Helvetici, vol. 26, pp. 328–344, 1952. \endinput