Table of Contents
ISRN Geometry
Volume 2013 (2013), Article ID 231869, 8 pages
http://dx.doi.org/10.1155/2013/231869
Research Article

Nonexistence of Totally Contact Umbilical Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

1School of Mathematics and Computer Applications, Thapar University, Patiala 147004, India
2University College of Engineering, Punjabi University, Patiala 147002, India

Received 1 April 2013; Accepted 12 May 2013

Academic Editors: A. Fino, C. Qu, and E. H. Saidi

Copyright © 2013 Rashmi Sachdeva 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, “Slant immersions,” Bulletin of the Australian Mathematical Society, vol. 41, no. 1, pp. 135–147, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B.-Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, Louvain, Belgium, 1990. View at Zentralblatt MATH · View at MathSciNet
  3. A. Lotta, “Slant submanifolds in contact geometry,” Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 39, pp. 183–198, 1996. View at Google Scholar
  4. A. Lotta, “Three-dimensional slant submanifolds of K-contact manifolds,” Balkan Journal of Geometry and Its Applications, vol. 3, no. 1, pp. 37–51, 1998. View at Google Scholar · View at MathSciNet
  5. J. L. Cabrerizo, A. Carriazo, L. M. Fernández, and M. Fernández, “Slant submanifolds in Sasakian manifolds,” Glasgow Mathematical Journal, vol. 42, no. 1, pp. 125–138, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. L. Cabrerizo, A. Carriazo, L. M. Fernández, and M. Fernández, “Semi-slant submanifolds of a Sasakian manifold,” Geometriae Dedicata, vol. 78, no. 2, pp. 183–199, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. B. Şahin, “Slant lightlike submanifolds of indefinite Hermitian manifolds,” Balkan Journal of Geometry and Its Applications, vol. 13, no. 1, pp. 107–119, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. S. Gupta, A. Upadhyay, and A. Sharfuddin, “Slant lightlike submanifolds of indefinite cosymplectic manifolds,” Mediterranean Journal of Mathematics, vol. 8, no. 2, pp. 215–227, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. V. Jain, R. Kumar, and R. K. Nagaich, “Non existence of totally contact umbilical GCR-lightlike submanifolds of indefinite cosymplectic manifolds,” Vietnam Journal of Mathematics, 2013. View at Publisher · View at Google Scholar
  10. R. Kumar, R. Rani, and R. K. Nagaich, “On sectional curvatures of ϵ-Sasakian manifolds,” International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 93562, 8 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  11. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, vol. 203 of Progress in Mathematics, Birkhäuser, Boston, Mass, USA, 2002. View at MathSciNet
  12. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, vol. 364 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. View at MathSciNet
  13. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, vol. 103 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1983. View at MathSciNet
  14. K. Yano and M. Kon, Structures on Manifolds, vol. 3 of Series in Pure Mathematics, World Scientific Publishing, Singapore, 1984. View at MathSciNet
  15. C. L. Bejan and K. L. Duggal, “Global lightlike manifolds and harmonicity,” Kodai Mathematical Journal, vol. 28, no. 1, pp. 131–145, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  16. K. L. Duggal and B. Sahin, “Screen Cauchy Riemann lightlike submanifolds,” Acta Mathematica Hungarica, vol. 106, no. 1-2, pp. 137–165, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet