Generic lightlike submanifolds of an indefinite Kaehler manifold with an $(\ell, m)$-type metric connection
DOI:
https://doi.org/10.52737/18291163-2020.12.6-1-17Keywords:
Generic lightlike submanifold, $(\ell, m)$-type metric connection, Indefinite Kaehler manifold, Indefinite complex space formAbstract
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. https://doi.org/10.1007/bf02564308
K.L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996. https://doi.org/10.1007/978-94-017-2089-2_5
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. https://doi.org/10.4134/bkms.2014.51.6.1711
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. https://doi.org/10.12988/ams.2015.52165
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. https://doi.org/10.4134/ckms.c150135
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. https://doi.org/10.4134/bkms.b150590
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. https://doi.org/10.17654/ms103081323
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. https://doi.org/10.1155/2011/610986
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. https://doi.org/10.12988/ijma.2015.5255
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
Versions
- 2022-08-30 (2)
- 2020-08-18 (1)
Issue
Section
License
Copyright (c) 2020 Armenian Journal of Mathematics
This work is licensed under a Creative Commons Attribution 4.0 International License.