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Journal of Mathematics
Volume 2013 (2013), Article ID 395787, 7 pages
http://dx.doi.org/10.1155/2013/395787
Research Article

Totally Contact Umbilical Lightlike Hypersurfaces of Indefinite -Manifolds

1University College, Moonak, Punjab 148033, India
2University College of Engineering, Punjabi University, Patiala 147002, India
3Department of Mathematics, Punjabi University, Patiala 147002, India

Received 22 August 2012; Revised 5 November 2012; Accepted 8 November 2012

Academic Editor: Mingsheng Liu

Copyright © 2013 Rachna Rani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, NY, USA, 1973.
  2. B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.
  3. K. L. Duggal and A. Bejancu, Lightlike SubManifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. View at MathSciNet
  4. K. L. Duggal and B. Sahin, “Lightlike submanifolds of indefinite Sasakian manifolds,” International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 57585, 21 pages, 2007. View at Google Scholar · View at Zentralblatt MATH
  5. V. I. Arnold, “Contact geometry: the geometrical method of Gibbss thermodynamics,” in Proceedings of the Gibbs Symposium, pp. 163–179, American Mathematical Society, New Haven, Conn, USA, 1989. View at Google Scholar
  6. S. Maclane, Geometrical Mechanics II, Lecture Notes, University of Chicago, Chicago, Ill, USA, 1968.
  7. V. E. Nazaikinskii, V. E. Shatalov, and B. Y. Sternin, Contact Geometry and Linear Differential Equations, vol. 6 of De Gruyter Expositions in Mathematics, Walter de Gruyter, Berlin, Germany, 1992.
  8. L. Brunetti and A. M. Pastore, “Curvature of a class of indefinite globally framed f-manifolds,” Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, vol. 51, no. 3, pp. 183–204, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. C. Calin, “On existence of degenerate hypersurfaces in Sasakian manifolds,” Arab Journal of Mathematical Sciences, vol. 5, pp. 21–27, 1999. View at Google Scholar · View at Zentralblatt MATH
  10. L. Brunetti and A. M. Pastore, “Lightlike hypersurfaces in indefiite 𝒮-manifolds,” Differential Geometry—Dynamical Systems, vol. 12, pp. 18–40, 2010. View at Google Scholar
  11. A. Bejancu, “Umbilical semi-invariant submanifolds of a Sasakian manifold,” Tensor, vol. 37, pp. 203–213, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet