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http://dx.doi.org/10.4134/CKMS.c190401

GEOMETRY OF HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE KAEHLER MANIFOLDS WITH A QUARTER-SYMMETRIC METRIC CONNECTION  

Gupta, Garima (Department of Basic and Applied Sciences Punjabi University)
Kumar, Rakesh (Department of Basic and Applied Sciences Punjabi University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.3, 2020 , pp. 979-998 More about this Journal
Abstract
We study totally umbilical real half lightlike submanifolds of indefinite Kaehler manifolds with a quarter-symmetric metric connection. We obtain some conditions for a real half lightlike submanifold of an indefinite Kaehler manifold with a quarter-symmetric metric connection to be a product manifold. We derive the expression for induced Ricci type tensor 𝓡(0,2) and also obtain conditions for 𝓡(0,2) to be symmetric.
Keywords
Indefinite Kaehler manifold; real half lightlike submanifolds; quarter-symmetric metric connection; null sectional curvature; induced Ricci type tensor;
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1 G. Gupta, R. Kumar, and R. K. Nagaich, Screen conformal lightlike submanifolds of semi-Riemannian manifolds, J. Geom. 107 (2016), no. 3, 635-655. https://doi.org/10.1007/s00022-015-0305-z   DOI
2 G. Gupta, R. Kumar, and R. K. Nagaich, Radical screen transversal lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection, Int. J. Geom. Methods Mod. Phys. 15 (2018), no. 2, 1850024, 21 pp. https://doi.org/10.1142/S021988781850024X
3 S. W. Hawking and G. F. R. Ellis, TheLarge Scale Structure of Spacetime, Cambridge University Press, London, 1973.
4 D. H. Jin, Geometry of screen conformal real half lightlike submanifolds, Bull. Korean Math. Soc. 47 (2010), no. 4, 701-714. https://doi.org/10.4134/BKMS.2010.47.4.701   DOI
5 G. Gupta, R. Kumar, and R. K. Nagaich, Geometry of half lightlike submanifolds of an indefinite Kaehler manifold with a quarter-symmetric metric connection, Honam Math. J. 36 (2014), no. 2, 217-232. https://doi.org/10.5831/HMJ.2014.36.2.217   DOI
6 G. Gupta, R. Kumar, and R. K. Nagaich, Lightlike hypersurfaces of an indefinite Kaehler manifold with a quarter-symmetric metric connection, Bull. Korean Math. Soc. 52 (2015), no. 1, 201-213. https://doi.org/10.4134/BKMS.2015.52.1.201   DOI
7 G. Gupta, R. Kumar, and R. K. Nagaich, Geometry of lightlike hypersurfaces of an indefinite Kaehler manifold with a quarter-symmetric metric connection, Appl. Math. Sci. 10 (2016), 289-299.
8 G. Gupta, R. Kumar, and R. K. Nagaich, Generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection, Bull. Korean Math. Soc. 54 (2017), no. 3, 1003-1022. https://doi.org/10.4134/BKMS.b160439   DOI
9 G. Gupta, R. Kumar, and R. K. Nagaich, Generic lightlike submanifolds of an indefinite Kaehler manifold with a quarter-symmetric metric connection, Bull. Korean Math. Soc. 55 (2018), no. 2, 515-531. https://doi.org/10.4134/BKMS.b170093   DOI
10 S. Kumar, R. Kumar, and R. K. Nagaich, Characterization of holomorphic bisectional curvature of GCR-lightlike submanifolds, Adv. Math. Phys. 2012 (2012), Art. ID 356263, 18 pp. https://doi.org/10.1155/2012/356263
11 R. S. Mishra and S. N. Pandey, On quarter symmetric metric F-connections, Tensor (N.S.) 34 (1980), no. 1, 1-7.
12 N. Pusic, On quarter-symmetric metric connections on a hyperbolic Kaehlerian space, Publ. Inst. Math. (Beograd) (N.S.) 73(87) (2003), 73-80. https://doi.org/10.2298/PIM0373073P   DOI
13 G. de Rham, Sur la reductibilite d'un espace de Riemann, Comment. Math. Helv. 26 (1952), 328-344. https://doi.org/10.1007/BF02564308   DOI
14 B. Sahin, Every totally umbilical proper slant submanifold of a Kahler manifold is totally geodesic, Results Math. 54 (2009), no. 1-2, 167-172. https://doi.org/10.1007/s00025-008-0324-2   DOI
15 K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.) 38 (1982), 13-18.
16 K. L. Duggal and D. H. Jin, Half lightlike submanifolds of codimension 2, Math. J. Toyama Univ. 22 (1999), 121-161.
17 M. Barros and A. Romero, Indefinite Kahler manifolds, Math. Ann. 261 (1982), no. 1, 55-62. https://doi.org/10.1007/BF01456410   DOI
18 J. K. Beem, P. E. Ehrlich, and K. L. Easley, Global Lorentzian Geometry, second edition, Monographs and Textbooks in Pure and Applied Mathematics, 202, Marcel Dekker, Inc., New York, 1996.
19 B. Chen, CR-submanifolds of a Kaehler manifold. I, J. Differential Geometry 16 (1981), no. 2, 305-322. http://projecteuclid.org/euclid.jdg/1214436106
20 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. https://doi.org/10.1007/978-94-017-2089-2
21 K. L. Duggal and D. H. Jin, Totally umbilical lightlike submanifolds, Kodai Math. J. 26 (2003), no. 1, 49-68. https://doi.org/10.2996/kmj/1050496648   DOI
22 K. L. Duggal and B. Sahin, Screen conformal half-lightlike submanifolds, Int. J. Math. Math. Sci. 68 (2004), no. 65-68, 3737-3753. https://doi.org/10.1155/S0161171204403342
23 K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser Verlag, Basel, 2010. https://doi.org/10.1007/978-3-0346-0251-8