Abstract
After brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product
References
[1] V. I. Arnold, Contact geometry: the geometrical method of Gibbs’s thermodynamodynamics,Proceedings of the Gibbs Symposium (New Haven, CT, 1989), 1990, 163-179.Search in Google Scholar
[2] A. Bejancu, CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc. 69(1978), 135-142.Search in Google Scholar
[3] A. Bejancu, CR-submanifolds of a Kaehler manifold-II, Trans. Amer. Math. Soc. 250(1979), 333-345.10.1090/S0002-9947-1979-0530059-6Search in Google Scholar
[4] A. Bejancu, M. Kon, K. Yano, CR-submanifolds of a complex space form, J. DifferentialGeom. 16 (1981), 137-145.Search in Google Scholar
[5] B. Y. Chen, CR-submanifolds of a Kaehler manifold-I, J. Differential Geom. 16 (1981),305-322.Search in Google Scholar
[6] B. Y. Chen, CR-submanifolds of a Kaehler manifold-II, J. Differential Geom. 16(1981), 493-509.Search in Google Scholar
[7] K. L. Duggal, A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds andapplications, Mathematics and its Applications 364, Kluwer Academic Publishers,1996.10.1007/978-94-017-2089-2Search in Google Scholar
[8] K. L. Duggal, B. Sahin, Lightlike submanifolds of indefinite Sasakian manifolds, Int.J. Math. Math. Sci. Vol. 2007, Article ID 57585, 21 pages.10.1155/2007/57585Search in Google Scholar
[9] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor (N.S.) 35 (1981),297-307.Search in Google Scholar
[10] R. Kumar, R. Rani, R. K. Nagaich, On sectional curvatures of p(∊)q-Sasakian manifolds,Int. J. Math. Math. Sci. Vol. 2007, Article ID 93562, 8 pages.10.1155/2007/93562Search in Google Scholar
[11] S. Maclane, Geometrical Mechanics II, Lecture Notes, University of Chicago, 1968.Search in Google Scholar
[12] V. E. Nazaikinskii, V. E. Shatalov, B. Y. Sternin, Contact Geometry and LinearDifferential Equations, De Gruyter Expositions in Mathematics 6, Walter de Gruyter,1992.10.1515/9783110873108Search in Google Scholar
[13] K. Yano, M. Kon, Contact CR-submanifolds, Kodai Math. J. 5 (1982), 238-252.10.2996/kmj/1138036553Search in Google Scholar
[14] K. Yano, M. Kon, CR-submanifolds of a Kaehlerien and Sasakian Manifolds, Birkhauser,Boston, 1983.10.1007/978-1-4684-9424-2Search in Google Scholar
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