Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds

Abstract

We study GCR-lightlike submanifolds of (ε)-Sasakian manifolds and derived some important structural characteristics equations for further uses. We also obtain some necessary and sufficient conditions for the integrability of various distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds.

Keywords

• ($\varepsilon$)-Sasakian manifold,lightlike submanifold,GCR-lightlike submanifold,degenerate metric

References

1. Bejancu, A. CR., Submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. (1978), 69: 135-142.
2. Bejancu, A., Duggal, KL. Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci. (1993), 16 : 546-556.
3. Duggal, KL. CR-Structures and Lorentzian geometry, Acta Appl. Math. (1986), 7: 211-223.
4. Duggal, KL. Lorentzian geometry of CR-submanifolds, Acta Appl. Math. (1989), 17: 171-193.
5. Duggal, KL., Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1996.
6. Duggal, KL., Sahin, B. Screen Cauchy-Riemann lightlike submanifolds, Acta Math. Hung. (2005), 106: 137-165.
7. Duggal, KL., Sahin, B. Generalized Cauchy Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hung. (2006), 112: 107-130.
8. Duggal, KL., Sahin, B. Generalized Cauchy Riemann lightlike submanifolds of indefinite Sasakian manifolds, Acta Math. Hung. (2009), 122: 45-58.

9. Kumar, R., Kumar, S., Nagaich, RK. On sectional curvatures of Sasakian manifolds, Int. J. Math. Math. Sci. (2007), 1-8.
10. Kumar, R., Kumar, S., Nagaich, RK. GCR-lightlike product of indefinite Kaehler manifolds, ISRN Geometry (2011), 1-13.
11. Kumar, R., Kumar, S., Nagaich, RK. Integrability of distributions in GCR-lightlike submanifolds of indefinite Kaehler manifolds, Commun. Korean Math. Soc. (2012), 27: 591-602.
12. Kumar, S., Kumar, R., Nagaich, RK. Characterization of holomorphic bisectional curvature of GCR-lightlike submanifolds, Adv. Math. Phys. (2012), 2012: 1-18.
13. Kumar, S., Kumar, R., Nagaich, RK. GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds, B. Korean Math. Soc. (2013), 50: 1173-1192.
14. Kumar, S., Kumar, R., Nagaich, RK. GCR-Lightlike Submanifolds of a Semi-Riemannian product manifold, B. Korean Math Soc. (2014), 51: 883-899.
15. Kumar, S., Kumar, R., Nagaich, RK. Ricci tensor for GCR-lightlike submanifolds of indefinite Kaehler manifolds, B. Iran Math. Soc. (2013), 39: 1009-1029.
16. Jain, V., Kumar, R., Nagaich, RK. Totally contact umbilical GCR-lightlike submanifolds of indefinite Sasakian manifolds, Vietnam J Math., (2011), 39: 91-103.
17. Jain, V., Kumar, R., Nagaich, RK. Integrability of distributions in GCR-lightlike submanifolds of indefinite Sasakian manifolds, Kyongpook Math. J. (2013), 53: 207-218.
18. Jain, V., Rani, R., Kumar, R., Nagaich, RK. Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds, Int J Geom Methods Mod Phys. (2017), 14: 1-18.