Research Article
BibTex RIS Cite

A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS

Year 2021, Volume: 4 Issue: 1, 25 - 33, 31.01.2021
https://doi.org/10.33773/jum.876269

Abstract

We study GCR-lightlike submanifolds of semi-Riemannian product manifolds. We give some equivalent conditions for the integrability of various distributions of GCR-lightlike submanifolds of semi-Riemannian product manifolds and investigate the geometry of leaves of distributions.

References

  • Atçeken, M. and Kılıç, E. Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifol, Kodai Math. J. Vol. 30, No. 3, (2007), pp. 361-378
  • Doğan, B., ¸Sahin, B., & Yaşar, E. (2019). Screen Generic Lightlike Submanifolds. Mediterranean Journal of Mathematics, 16(4), 104.
  • Duggal, K. L., Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic Publishers, Dordrecht (1996)
  • Duggal, K. L., Şahin B.: Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hung. 106(1-2), 125–153 (2005)
  • Duggal, K. L., Şahin B.: Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. Acta Math. Hung. 112(1-2), 107-130 (2006)
  • Duggal, K. L., Şahin, B.: Generalized Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds. Acta Math. Hung. 122(1-2), 45-58 (2009)
  • Duggal, K. L., Şahin B.: Di¤erential Geometry of Lightlike Submanifolds. Birkhäuser, Basel (2010)
  • Gupta, R.S., Sharfuddin, A.: Generalised Cauchy-Riemann lightlike submanifolds of indefinite Kenmotsu manifolds. Note di Matematica 30(2), 49-60 (2011).
  • Gupta, R.S., Upadhyay, A., Sharfuddin, A.: Generalised Cauchy-Riemann lightlike submanifolds of inde…nite cosymplectic manifolds. An. ¸Stiin¸t. Univ. Al. I. CuzaIa¸si. Mat. (N.S.), 58(2), 381-394 (2012).
  • Khursheed Haider S. M., Thakur, M. and Advin, Screen Cauchy-Riemann lightlike submanifolds of a semi-Riemannian product manifold, Int. Electron. J. Geom. 4, no. 2, 141-155, (2011)
  • Kılıç, E., & Şahin, B. Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds. Turkish Journal of Mathematics, 32(4), 429-449,(2008).
  • Kılıç, E., Şahin, B. and Keleş, S., Screen semi-invariant lightlike submanifolds of a semi-Riemannian product manifolds, Int. Electron. J. Geom. 4 , 120-135, (2011).
  • Kumar, R., Jain, V., Nagaich, R. K., GCR-lightlike product of inde…nite Sasakian manifolds. Advances in Mathematical Physics, 2011, Article ID 983069, 1-13 (2011)
  • Kumar, R., Kumar, S., & Nagaich, R. K. Integrability of distributions in GCR-lightlike submanifolds of inde…nite Kaehler manifolds. Communications of the Korean Mathematical Society, 27(3), 591-602, (2012).
  • Kumar, S., Kumar, R., Nagaich, R. K.: GCR-lightlike submanifolds of a semi-Riemannian product manifold. Bull. Korean Math. Soc. 51(3), 883-899 (2014)
  • D. N. Kupeli, Singular Semi-Riemannian Geometry, vol. 366, Kluwer, Dordrecht, 1996.
  • Perkta¸s, S. Y., Kılıç, E., Keleş, S., Warped product submanifolds of Lorentzian paracosymplectic manifolds. Arabian Journal of Mathematics, 1(3), 377-393, (2012).
  • Poyraz, N. Ö. Golden GCR-Lightlike Submanifolds of Golden Semi-Riemannian Manifolds. Mediterranean Journal of Mathematics, 17(5), 1-16 (2020).
  • Senlin, X. and Yilong, N., Submanifolds of Product Riemannian Manifold. Acta Mathematica Scientia, 20(B), 213-218, (2000).
  • Şahin, B. Lightlike submanifolds of indefinite quaternion Kaehler manifolds. Demonstratio Mathematica, 40(3), 701-720, (2007).
Year 2021, Volume: 4 Issue: 1, 25 - 33, 31.01.2021
https://doi.org/10.33773/jum.876269

Abstract

References

  • Atçeken, M. and Kılıç, E. Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifol, Kodai Math. J. Vol. 30, No. 3, (2007), pp. 361-378
  • Doğan, B., ¸Sahin, B., & Yaşar, E. (2019). Screen Generic Lightlike Submanifolds. Mediterranean Journal of Mathematics, 16(4), 104.
  • Duggal, K. L., Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic Publishers, Dordrecht (1996)
  • Duggal, K. L., Şahin B.: Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hung. 106(1-2), 125–153 (2005)
  • Duggal, K. L., Şahin B.: Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. Acta Math. Hung. 112(1-2), 107-130 (2006)
  • Duggal, K. L., Şahin, B.: Generalized Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds. Acta Math. Hung. 122(1-2), 45-58 (2009)
  • Duggal, K. L., Şahin B.: Di¤erential Geometry of Lightlike Submanifolds. Birkhäuser, Basel (2010)
  • Gupta, R.S., Sharfuddin, A.: Generalised Cauchy-Riemann lightlike submanifolds of indefinite Kenmotsu manifolds. Note di Matematica 30(2), 49-60 (2011).
  • Gupta, R.S., Upadhyay, A., Sharfuddin, A.: Generalised Cauchy-Riemann lightlike submanifolds of inde…nite cosymplectic manifolds. An. ¸Stiin¸t. Univ. Al. I. CuzaIa¸si. Mat. (N.S.), 58(2), 381-394 (2012).
  • Khursheed Haider S. M., Thakur, M. and Advin, Screen Cauchy-Riemann lightlike submanifolds of a semi-Riemannian product manifold, Int. Electron. J. Geom. 4, no. 2, 141-155, (2011)
  • Kılıç, E., & Şahin, B. Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds. Turkish Journal of Mathematics, 32(4), 429-449,(2008).
  • Kılıç, E., Şahin, B. and Keleş, S., Screen semi-invariant lightlike submanifolds of a semi-Riemannian product manifolds, Int. Electron. J. Geom. 4 , 120-135, (2011).
  • Kumar, R., Jain, V., Nagaich, R. K., GCR-lightlike product of inde…nite Sasakian manifolds. Advances in Mathematical Physics, 2011, Article ID 983069, 1-13 (2011)
  • Kumar, R., Kumar, S., & Nagaich, R. K. Integrability of distributions in GCR-lightlike submanifolds of inde…nite Kaehler manifolds. Communications of the Korean Mathematical Society, 27(3), 591-602, (2012).
  • Kumar, S., Kumar, R., Nagaich, R. K.: GCR-lightlike submanifolds of a semi-Riemannian product manifold. Bull. Korean Math. Soc. 51(3), 883-899 (2014)
  • D. N. Kupeli, Singular Semi-Riemannian Geometry, vol. 366, Kluwer, Dordrecht, 1996.
  • Perkta¸s, S. Y., Kılıç, E., Keleş, S., Warped product submanifolds of Lorentzian paracosymplectic manifolds. Arabian Journal of Mathematics, 1(3), 377-393, (2012).
  • Poyraz, N. Ö. Golden GCR-Lightlike Submanifolds of Golden Semi-Riemannian Manifolds. Mediterranean Journal of Mathematics, 17(5), 1-16 (2020).
  • Senlin, X. and Yilong, N., Submanifolds of Product Riemannian Manifold. Acta Mathematica Scientia, 20(B), 213-218, (2000).
  • Şahin, B. Lightlike submanifolds of indefinite quaternion Kaehler manifolds. Demonstratio Mathematica, 40(3), 701-720, (2007).
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Nergiz Poyraz

Publication Date January 31, 2021
Submission Date February 7, 2021
Acceptance Date February 13, 2021
Published in Issue Year 2021 Volume: 4 Issue: 1

Cite

APA Poyraz, N. (2021). A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. Journal of Universal Mathematics, 4(1), 25-33. https://doi.org/10.33773/jum.876269
AMA Poyraz N. A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. JUM. January 2021;4(1):25-33. doi:10.33773/jum.876269
Chicago Poyraz, Nergiz. “A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”. Journal of Universal Mathematics 4, no. 1 (January 2021): 25-33. https://doi.org/10.33773/jum.876269.
EndNote Poyraz N (January 1, 2021) A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. Journal of Universal Mathematics 4 1 25–33.
IEEE N. Poyraz, “A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”, JUM, vol. 4, no. 1, pp. 25–33, 2021, doi: 10.33773/jum.876269.
ISNAD Poyraz, Nergiz. “A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”. Journal of Universal Mathematics 4/1 (January 2021), 25-33. https://doi.org/10.33773/jum.876269.
JAMA Poyraz N. A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. JUM. 2021;4:25–33.
MLA Poyraz, Nergiz. “A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”. Journal of Universal Mathematics, vol. 4, no. 1, 2021, pp. 25-33, doi:10.33773/jum.876269.
Vancouver Poyraz N. A STUDY ON GCR-LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. JUM. 2021;4(1):25-33.