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http://dx.doi.org/10.4134/CKMS.c180128

GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH AN (ℓ, m)-TYPE METRIC CONNECTION  

Jin, Dae Ho (Department of Mathematics Education Dongguk University)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 615-632 More about this Journal
Abstract
We study generic lightlike submanifolds M of an indefinite trans-Sasakian manifold ${\bar{M}}$ or an indefinite generalized Sasakian space form ${\bar{M}}(f_1,f_2,f_3)$ endowed with an $({\ell},m)$-type metric connection subject such that the structure vector field ${\zeta}$ of ${\bar{M}}$ is tangent to M.
Keywords
$({\ell},m)$-type metric connection; generic lightlike submanifold; indefinite trans-Sasakian structure;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 K. L. Duggal and D. J. Jin, Generic lightlike submanifolds of an indefinite Sasakian manifold, Int. Electron. J. Geom. 5 (2012), no. 1, 108-119.
2 H. A. Hayden, Sub-spaces of a space with torsion, Proc. London Math. Soc. (2) 34 (1932), no. 1, 27-50.   DOI
3 D. H. Jin, Indefinite generalized Sasakian space form admitting a generic lightlike submanifold, Bull. Korean Math. Soc. 51 (2014), no. 6, 1711-1726.   DOI
4 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.
5 D. H. Jin, Lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an ($\ell$, m)-type metric connection, Far East J. Math. Sci. 103 (2018), no. 8, 1323-1343.   DOI
6 D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite cosymplectic manifold, Math. Probl. Eng. 2011 (20111), Art. ID 610986, 16 pp.
7 D. H. Jin and J. W. Lee, Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature, Filomat 30 (2016), no. 7, 1737-1745.   DOI
8 D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite Kaehler manifold, Inter. J. Pure Appl. Math. 101 (2015), no. 4, 543-560.
9 D. N. Kupeli, Singular Semi-Riemannian Geometry, Mathematics and its Applications, 366, Kluwer Academic Publishers Group, Dordrecht, 1996.
10 J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187-193.
11 K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.
12 K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.) 38 (1982), 13-18.
13 K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and its Applications, 364, Kluwer Academic Publishers Group, Dordrecht, 1996.
14 P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math. 141 (2004), 157-183.   DOI
15 C. Calin, Contributions to geometry of CR-submanifold, Thesis, University of Iasi, Romania, 1998.
16 G. de Rham, Sur la reductibilite d'un espace de Riemann, Comment. Math. Helv. 26 (1952), 328-344.   DOI