This is an outdated version published on 2020-08-18. Read the most recent version.

Generic lightlike submanifolds of an indefinite Kaehler manifold with an $(\ell, m)$-type metric connection

Authors

  • Chul Woo Lee Kyungpook National University
  • Jae Won Lee Gyeongsang National University

DOI:

https://doi.org/10.52737/18291163-2020.12.6-1-17

Keywords:

Generic lightlike submanifold, $(\ell, m)$-type metric connection, Indefinite Kaehler manifold, Indefinite complex space form

Abstract

We study generic lightlike submanifolds $M$ of an indefinite Kaehler manifold $\bar{M}$ or an indefinite complex space form $\bar{M}(c)$ with an $(\ell, m)$-type metric connection subject such that the characteristic vector field $\zeta$ of $\bar{M}$ belongs to our screen distribution $S(TM)$ of $M$.

References

G. de Rham, Sur la reeductibilite d'un espace de Riemannian, Comm. Math. Helv., 26 (1952), 328-344.

K.L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.

K.L. Duggal and D.H. Jin, Generic lightlike submanifolds of an indefinite Sasakian manifold, Int. Elec. J. Geo., 5 (2012), no. 1, 108-119.

H.A. Hayden, Subspace of a space with torsion, Proc. London Math. Soc., 34 (1932), 27-50.

D.H. Jin, Indefinite generalized Sasakian space form admitting a generic lightlike submanifold, Bull. Korean Math. Soc., 51 (2014), no. 6, 1711-1726.

D.H. Jin, Generic lightlike submanifolds of an indefinite trans-Sasakian manifold of a quasi-constant curvature, Appl. Math. Sci., 9 (2015), no. 60, 2985-2997.

D.H. Jin, Lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (l, m), Commun. Korean Math. Soc., 31 (2016), no. 3, 613-624.

D.H. Jin, Lightlike hypersurfaces of an indefinite Kaehler manifold with a symmetric metric connection of type (l, m), Bull. Korean Math. Soc., 53 (2016), no. 4, 1171-1184.

D.H. Jin, Lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (l,m)-type metric connection, Far East J. Math. Sci., 103 (2008), no. 8, 1323-1343.

D.H. Jin and J.W. Lee, Generic lightlike submanifolds of an indefinite cosymplectic manifold, Math. Probl. in Engin., 2011 (2011), Art ID 610986, 1-16.

D.H. Jin and J.W. Lee, Generic lightlike submanifolds of an indefinite Kaehler manifold, Inter. J. Pure and Appl. Math., 101 (2015), no. 4, 543-560.

D.H. Jin and J.W. Lee, A semi-Riemannian manifold of quasi-constant curvature admits lightlike submanifolds, Inter. J. of Math. Analysis, 9 (2015), no. 26, 1215-1229.

D.N. Kupeli, Singular Semi-Riemannian Geometry, Kluwer Academic, 1996.

K. Yano, On semi-symmetric metric connection, Rev. Roum. Math. Pures et Appl., 15 (1970), 1579-1586.

K. Yano and T. Imai, Quarter-symmetric metric connection and their curvature tensors, Tensor, N.S., 38 (1982), 13-18.

Downloads

Published

2020-08-18

Versions

How to Cite

Generic lightlike submanifolds of an indefinite Kaehler manifold with an $(\ell, m)$-type metric connection. (2020). Armenian Journal of Mathematics, 12(6), 1-17. http://test.armjmath.sci.am/index.php/ajm/article/view/370