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Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. (English) Zbl 1296.53041
Summary: In this paper we prove some properties of indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define \(D\)-totally geodesic and \(D^\bot\)-totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold.
MSC:
53B25 Local submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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[1] A. Bejancu, CR-submanifolds of a Kaehlerian manifold I, Proc. Amer. Math. Soc., 69 (1978), 135-142. · Zbl 0368.53040
[2] A. Bejancu, CR-submanifolds of a Kaehlerian manifold II, Trans. Amer. Math. Soc., 250 (1979), 333-345. · Zbl 0368.53041
[3] A. Bhattacharyya, B. Das, Contact CR-submanifolds of an indefinite trans-Sasakian manifold, Int. J. Contemp. Math. Sci, 6 (26) (2011), 1271-1282 · Zbl 1247.53022
[4] A. Bejancu, K. L. Duggal, Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci. , 16 (3) (1993), 545-556. · Zbl 0787.53048
[5] D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Mathematics, vol. 509, Springer Verlag, Berlin, (1976). · Zbl 0319.53026
[6] C. Calin, I. Mihai, On a normal contact metric manifold, Kyungpook Math. J. 45 (2005), 55-65. · Zbl 1087.53022
[7] B. Y. Chen, Geometry of submanifolds, M. Dekker, New York, (1973).
[8] B. Y. Chen, K. Ogiue, On totally real submanifolds, Trans. Amer. Math. Soc., 193 (1974), 257-266. · Zbl 0286.53019
[9] K. L. Duggal, A. Bejancu, Lightlike submanifold of semi-Riemannian Manifolds and Applications, vol. 364 of Mathematics and its applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. · Zbl 0848.53001
[10] K. L. Duggal, B. Sahin, Lightlike submanifolds of indefinite Sasakian manifolds, Int. J. Math. Math. Sci., (2007), 1-22. · Zbl 1147.53044
[11] T. H. Kang, S. D. Jung, B. H. Kim, Lightlike hypersurfaces of indefinite Sasakian manifolds, Indian J. Pure Appl. Math., 34 (9) (2003), 1369-1380. · Zbl 1046.53053
[12] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor, N. S., 35 (1981), 297-307. · Zbl 0484.53048
[13] M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), 277-290. · Zbl 0301.53031
[14] G. D. Ludden, Submanifolds of cosymplectic manifolds, Jour. of Diff. Geom., 4 (1970), 237-244. · Zbl 0197.47902
[15] K. Matsumoto, On Lorentzian para contact manifolds, Bull. Yamagata Univ. Nat. Sci., 12 (1989), 151-156. · Zbl 0675.53035
[16] K. Matsumoto, I. Mihai, On certain transformation in a Lorentzian para-Sasakian manifold, Tensor N. S., 47 (1968), 189-197. · Zbl 0679.53034
[17] K. Ogiue, Differential geometry of Kaehler submanifolds, Adv. Math., 13 (1974). · Zbl 0275.53035
[18] J. A. Oubi˜na, New classes of almost contact metric structures, Publ. Math. Debrecen, 32 (3-4), (1985), 187-193. · Zbl 0611.53032
[19] R. Prasad, V. Srivastava, On ε Lorentzian para-Sasakian manifolds, Commun. Korean Math. Soc. 27 (2) (2012), 297-306. · Zbl 1239.53040
[20] M. Tarafdar, A. Bhattacharya, On Lorentzian para-Sasakian manifolds, Steps in differential geometry, Proceedings of the Colloquium on Differential Geometry, 25-30 july 2000, Debrecen, Hungary, 343-348.
[21] K. Yano, M. Kon, Anti-invariant submanifolds, Marcel Dekker Inc., New York, (1976). · Zbl 0349.53055
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