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INTEGRABILITY OF DISTRIBUTIONS IN GCR-LIGHTLIKE SUBMANIFOLDS

Year 2013, Volume: 1 Issue: 2, 1 - 10, 01.12.2013

Abstract

We give necessary and sufficient conditions for the integrability ofvarious distributions of GCR-lightlike submanifold of an indefinite Kenmotsumanifold. We also find the conditions for each leaf of holomorphic distributionand radical distribution to be totally geodesic in submanifold

References

  • Blair, David E., Riemannian Geometry of Contact and Symplectic Manifolds. New York, Birkhauser (2002).
  • Calin, C., On Existence of Degenerate Hypersurfaces in Sasakian Manifolds. Arab J. Math. Sci. 5 (1999), 21–27.
  • Duggal, Krishan L. and Bejancu, A., Lightlike Submanifolds of semi-Riemannian Manifolds and Applications. Vol. 364 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  • Duggal, Krishan L. and S¸ahin, B., Lightlike Submanifolds of Indefinite Sasakian Manifolds. Int. J. Math. Math. Sci. Vol 2007, Article ID 57585, 21 pages.
  • Duggal, Krishan L. and S¸ahin, B., Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Sasakian Manifolds. Acta Math. Hungar. 122 (2009), 45–58.
  • Gupta, Ram S. and Sharfuddin, A., Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Kenmotsu Manifolds. Note Mat. 30 (2010), 4959.
  • Kumar, Rakesh, Rani, Rachna and Nagaich, Rakesh K., On Sectional curvature of -Sasakian Manifolds. Int. J. Math. Math. Sci. Vol 2007, Article ID 93562, 8 pages.
  • S¸ahin, B. and G¨une¸s, R., Integrebility of Distributions in CR-lightlike Submanifolds. Tamkang J. Math. 33 (2002), no. 3, 209-221.
  • Kumar, Sangeet, Kumar, Rakesh and Nagaich, Rakesh K., Integrebility of Distributions in GCR-lightlike Submanifolds of Indefinite Kaehler Manifolds. Commun. Korean Math. Soc. 27 (2012), no. 3, 591-602..
  • Jain, Varun, Kumar, Rakesh and Nagaich, Rakesh K., Integrability of distributions in GCR
  • lightlike submanifolds of indefinite Cosymplectic manifolds, Lobachevskii Journal of Mathe
  • matics. 34 (2013), no. 1, 76-84.
  • Multani Mal Modi College, Patiala, India.
  • E-mail address: varun82jain@gmail.com
  • University College of Engineering, Punjabi University, Patiala, India.
  • E-mail address: dr rk37c@yahoo.co.in
  • Department of Mathematics, Punjabi University, Patiala, India.
  • E-mail address: rakeshnagaich@yahoo.com

Year 2013, Volume: 1 Issue: 2, 1 - 10, 01.12.2013

Abstract

References

  • Blair, David E., Riemannian Geometry of Contact and Symplectic Manifolds. New York, Birkhauser (2002).
  • Calin, C., On Existence of Degenerate Hypersurfaces in Sasakian Manifolds. Arab J. Math. Sci. 5 (1999), 21–27.
  • Duggal, Krishan L. and Bejancu, A., Lightlike Submanifolds of semi-Riemannian Manifolds and Applications. Vol. 364 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  • Duggal, Krishan L. and S¸ahin, B., Lightlike Submanifolds of Indefinite Sasakian Manifolds. Int. J. Math. Math. Sci. Vol 2007, Article ID 57585, 21 pages.
  • Duggal, Krishan L. and S¸ahin, B., Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Sasakian Manifolds. Acta Math. Hungar. 122 (2009), 45–58.
  • Gupta, Ram S. and Sharfuddin, A., Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Kenmotsu Manifolds. Note Mat. 30 (2010), 4959.
  • Kumar, Rakesh, Rani, Rachna and Nagaich, Rakesh K., On Sectional curvature of -Sasakian Manifolds. Int. J. Math. Math. Sci. Vol 2007, Article ID 93562, 8 pages.
  • S¸ahin, B. and G¨une¸s, R., Integrebility of Distributions in CR-lightlike Submanifolds. Tamkang J. Math. 33 (2002), no. 3, 209-221.
  • Kumar, Sangeet, Kumar, Rakesh and Nagaich, Rakesh K., Integrebility of Distributions in GCR-lightlike Submanifolds of Indefinite Kaehler Manifolds. Commun. Korean Math. Soc. 27 (2012), no. 3, 591-602..
  • Jain, Varun, Kumar, Rakesh and Nagaich, Rakesh K., Integrability of distributions in GCR
  • lightlike submanifolds of indefinite Cosymplectic manifolds, Lobachevskii Journal of Mathe
  • matics. 34 (2013), no. 1, 76-84.
  • Multani Mal Modi College, Patiala, India.
  • E-mail address: varun82jain@gmail.com
  • University College of Engineering, Punjabi University, Patiala, India.
  • E-mail address: dr rk37c@yahoo.co.in
  • Department of Mathematics, Punjabi University, Patiala, India.
  • E-mail address: rakeshnagaich@yahoo.com
There are 18 citations in total.

Details

Primary Language English
Authors

Varun Jaın This is me

Rakeshkumar This is me

R. K.nagaıch This is me

Submission Date March 9, 2015
Publication Date December 1, 2013
Published in Issue Year 2013 Volume: 1 Issue: 2

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