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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero

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Volume 47, Issue 1


On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

Manish Gogna / Rakesh Kumar / R. K. Nagaich
Published Online: 2014-03-07 | DOI: https://doi.org/10.2478/dema-2014-0014


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

Keywords: indefinite Sasakian manifolds; lightlike submanifolds; contact CR-lightlike submanifolds; totally contact umbilical submanifolds


  • [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.Google Scholar

  • [2] A. Bejancu, CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc. 69(1978), 135-142.Google Scholar

  • [3] A. Bejancu, CR-submanifolds of a Kaehler manifold-II, Trans. Amer. Math. Soc. 250(1979), 333-345.Google Scholar

  • [4] A. Bejancu, M. Kon, K. Yano, CR-submanifolds of a complex space form, J. DifferentialGeom. 16 (1981), 137-145.Google Scholar

  • [5] B. Y. Chen, CR-submanifolds of a Kaehler manifold-I, J. Differential Geom. 16 (1981),305-322.Google Scholar

  • [6] B. Y. Chen, CR-submanifolds of a Kaehler manifold-II, J. Differential Geom. 16(1981), 493-509.Google Scholar

  • [7] K. L. Duggal, A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds andapplications, Mathematics and its Applications 364, Kluwer Academic Publishers,1996.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.Google Scholar

  • [9] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor (N.S.) 35 (1981),297-307.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.Google Scholar

  • [11] S. Maclane, Geometrical Mechanics II, Lecture Notes, University of Chicago, 1968.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.Google Scholar

  • [13] K. Yano, M. Kon, Contact CR-submanifolds, Kodai Math. J. 5 (1982), 238-252.Google Scholar

  • [14] K. Yano, M. Kon, CR-submanifolds of a Kaehlerien and Sasakian Manifolds, Birkhauser,Boston, 1983.Google Scholar

About the article

Published Online: 2014-03-07

Published in Print: 2014-03-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 1, Pages 170–178, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0014.

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© 2015 by Walter de Gruyter Berlin/Boston. This content is open access.

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