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Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds

Year 2020, Volume: 69 Issue: 1, 354 - 368, 30.06.2020
https://doi.org/10.31801/cfsuasmas.469747

Abstract

We study GCR-lightlike submanifolds of (ε)-Sasakian manifolds and derived some important structural characteristics equations for further uses. We also obtain some necessary and sufficient conditions for the integrability of various distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds.

References

  • Bejancu, A. CR., Submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. (1978), 69: 135-142.
  • Bejancu, A., Duggal, KL. Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci. (1993), 16 : 546-556.
  • Duggal, KL. CR-Structures and Lorentzian geometry, Acta Appl. Math. (1986), 7: 211-223.
  • Duggal, KL. Lorentzian geometry of CR-submanifolds, Acta Appl. Math. (1989), 17: 171-193.
  • Duggal, KL., Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1996.
  • Duggal, KL., Sahin, B. Screen Cauchy-Riemann lightlike submanifolds, Acta Math. Hung. (2005), 106: 137-165.
  • Duggal, KL., Sahin, B. Generalized Cauchy Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hung. (2006), 112: 107-130.
  • Duggal, KL., Sahin, B. Generalized Cauchy Riemann lightlike submanifolds of indefinite Sasakian manifolds, Acta Math. Hung. (2009), 122: 45-58.
  • Kumar, R., Kumar, S., Nagaich, RK. On sectional curvatures of Sasakian manifolds, Int. J. Math. Math. Sci. (2007), 1-8.
  • Kumar, R., Kumar, S., Nagaich, RK. GCR-lightlike product of indefinite Kaehler manifolds, ISRN Geometry (2011), 1-13.
  • Kumar, R., Kumar, S., Nagaich, RK. Integrability of distributions in GCR-lightlike submanifolds of indefinite Kaehler manifolds, Commun. Korean Math. Soc. (2012), 27: 591-602.
  • Kumar, S., Kumar, R., Nagaich, RK. Characterization of holomorphic bisectional curvature of GCR-lightlike submanifolds, Adv. Math. Phys. (2012), 2012: 1-18.
  • Kumar, S., Kumar, R., Nagaich, RK. GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds, B. Korean Math. Soc. (2013), 50: 1173-1192.
  • Kumar, S., Kumar, R., Nagaich, RK. GCR-Lightlike Submanifolds of a Semi-Riemannian product manifold, B. Korean Math Soc. (2014), 51: 883-899.
  • Kumar, S., Kumar, R., Nagaich, RK. Ricci tensor for GCR-lightlike submanifolds of indefinite Kaehler manifolds, B. Iran Math. Soc. (2013), 39: 1009-1029.
  • Jain, V., Kumar, R., Nagaich, RK. Totally contact umbilical GCR-lightlike submanifolds of indefinite Sasakian manifolds, Vietnam J Math., (2011), 39: 91-103.
  • Jain, V., Kumar, R., Nagaich, RK. Integrability of distributions in GCR-lightlike submanifolds of indefinite Sasakian manifolds, Kyongpook Math. J. (2013), 53: 207-218.
  • Jain, V., Rani, R., Kumar, R., Nagaich, RK. Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds, Int J Geom Methods Mod Phys. (2017), 14: 1-18.
Year 2020, Volume: 69 Issue: 1, 354 - 368, 30.06.2020
https://doi.org/10.31801/cfsuasmas.469747

Abstract

References

  • Bejancu, A. CR., Submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. (1978), 69: 135-142.
  • Bejancu, A., Duggal, KL. Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci. (1993), 16 : 546-556.
  • Duggal, KL. CR-Structures and Lorentzian geometry, Acta Appl. Math. (1986), 7: 211-223.
  • Duggal, KL. Lorentzian geometry of CR-submanifolds, Acta Appl. Math. (1989), 17: 171-193.
  • Duggal, KL., Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1996.
  • Duggal, KL., Sahin, B. Screen Cauchy-Riemann lightlike submanifolds, Acta Math. Hung. (2005), 106: 137-165.
  • Duggal, KL., Sahin, B. Generalized Cauchy Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hung. (2006), 112: 107-130.
  • Duggal, KL., Sahin, B. Generalized Cauchy Riemann lightlike submanifolds of indefinite Sasakian manifolds, Acta Math. Hung. (2009), 122: 45-58.
  • Kumar, R., Kumar, S., Nagaich, RK. On sectional curvatures of Sasakian manifolds, Int. J. Math. Math. Sci. (2007), 1-8.
  • Kumar, R., Kumar, S., Nagaich, RK. GCR-lightlike product of indefinite Kaehler manifolds, ISRN Geometry (2011), 1-13.
  • Kumar, R., Kumar, S., Nagaich, RK. Integrability of distributions in GCR-lightlike submanifolds of indefinite Kaehler manifolds, Commun. Korean Math. Soc. (2012), 27: 591-602.
  • Kumar, S., Kumar, R., Nagaich, RK. Characterization of holomorphic bisectional curvature of GCR-lightlike submanifolds, Adv. Math. Phys. (2012), 2012: 1-18.
  • Kumar, S., Kumar, R., Nagaich, RK. GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds, B. Korean Math. Soc. (2013), 50: 1173-1192.
  • Kumar, S., Kumar, R., Nagaich, RK. GCR-Lightlike Submanifolds of a Semi-Riemannian product manifold, B. Korean Math Soc. (2014), 51: 883-899.
  • Kumar, S., Kumar, R., Nagaich, RK. Ricci tensor for GCR-lightlike submanifolds of indefinite Kaehler manifolds, B. Iran Math. Soc. (2013), 39: 1009-1029.
  • Jain, V., Kumar, R., Nagaich, RK. Totally contact umbilical GCR-lightlike submanifolds of indefinite Sasakian manifolds, Vietnam J Math., (2011), 39: 91-103.
  • Jain, V., Kumar, R., Nagaich, RK. Integrability of distributions in GCR-lightlike submanifolds of indefinite Sasakian manifolds, Kyongpook Math. J. (2013), 53: 207-218.
  • Jain, V., Rani, R., Kumar, R., Nagaich, RK. Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds, Int J Geom Methods Mod Phys. (2017), 14: 1-18.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Ayşe Funda Saglamer This is me 0000-0001-5162-6378

Nesrin Çalışkan 0000-0002-3189-177X

Publication Date June 30, 2020
Submission Date October 12, 2018
Acceptance Date November 11, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Saglamer, A. F., & Çalışkan, N. (2020). Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 354-368. https://doi.org/10.31801/cfsuasmas.469747
AMA Saglamer AF, Çalışkan N. Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):354-368. doi:10.31801/cfsuasmas.469747
Chicago Saglamer, Ayşe Funda, and Nesrin Çalışkan. “Integrability of the Distributions of GCR-Lightlike Submanifolds of (ε)-Sasakian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 354-68. https://doi.org/10.31801/cfsuasmas.469747.
EndNote Saglamer AF, Çalışkan N (June 1, 2020) Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 354–368.
IEEE A. F. Saglamer and N. Çalışkan, “Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 354–368, 2020, doi: 10.31801/cfsuasmas.469747.
ISNAD Saglamer, Ayşe Funda - Çalışkan, Nesrin. “Integrability of the Distributions of GCR-Lightlike Submanifolds of (ε)-Sasakian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 354-368. https://doi.org/10.31801/cfsuasmas.469747.
JAMA Saglamer AF, Çalışkan N. Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:354–368.
MLA Saglamer, Ayşe Funda and Nesrin Çalışkan. “Integrability of the Distributions of GCR-Lightlike Submanifolds of (ε)-Sasakian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 354-68, doi:10.31801/cfsuasmas.469747.
Vancouver Saglamer AF, Çalışkan N. Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):354-68.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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