Research Article
BibTex RIS Cite

Screen generic lightlike submanifolds of semi-Riemannian product manifolds

Year 2024, Volume: 53 Issue: 1, 171 - 183, 29.02.2024

Nergiz Poyraz

https://doi.org/10.15672/hujms.1168604

Abstract

In this paper, we introduce screen generic lightlike submanifolds of semi-Riemannian product manifolds. We investigate the integrability of various distributions and geometry of such submanifolds. Finally, we find a condition for minimal screen generic lightlike submanifolds. We also give examples.

Keywords

semi-Riemannian product manifold lightlike submanifold generic lightlike submanifold minimal lightlike submanifold

References

  • [1] M. Atçeken and E. Kılıç, Semi-invariant Lightlike submanifolds of a semi-Riemannian product manifold, Kodai. Math. J. 30 (3), 361-378, 2007.
  • [2] C.L. Bejan and K.L. Duggal, Global lightlike manifolds and harmonicity, Kodai. Math. J. 28, 131–145, 2005.
  • [3] B. Dogan, B. Sahin and E. Yasar, Screen generic lightlike submanifolds, Mediterr. J. Math. 16 (4), 21, 2019.
  • [4] K.L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and Its Applications, Kluwer Publisher, 1996.
  • [5] K.L. Duggal and B. Sahin, Screen cauchy Riemann lightlike submanifolds, Acta Math. Hung. 106 (1), 137-165, 2005.
  • [6] K.L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hung. 112 (1-2), 107–130, 2006.
  • [7] K.L. Duggal and B. Sahin, Lightlike submanifolds of indefinite Sasakian manifolds, Int. J. Math. Math. Sci. 2007, Art. No. 57585, 2007.
  • [8] K.L. Duggal and B. Sahin, Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Sasakian Manifolds, Acta Math. Hung. 122, 45–58, 2009.
  • [9] K.L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, 2010.
  • [10] F.E. Erdogan, On some types of lightlike submanifolds of golden semi-Riemannian manifolds, Filomat 33 (10), 3231-3242, 2019.
  • [11] F.E. Erdogan, S.Y. Perktas, B.E. Acet and A.M. Blaga, Screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds, J. Geom. Phys. 142, 111-120, 2019.
  • [12] R.S. Gupta and A. Sharfuddin, Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Kenmotsu Manifolds, Note Mat. 30 (2), 49–59, 2010.
  • [13] R.S. Gupta, Screen Generic Lightlike Submanifolds of Indefinite Sasakian Manifolds, Mediterr. J. Math. 17 (5), 1-23, 2020.
  • [14] R.S. Gupta and A. Sharfuddin, Screen transversal lightlike submanifolds of indefinite cosymplectic manifolds, Rend. Semin. Mat. Univ. Padova, 124, 145-156, 2010.
  • [15] R.S. Gupta, A. Upadhyay and A. Sharfuddin, Generalised Cauchy-Riemann lightlike submanifolds of indefinite cosymplectic manifolds, Analele Stiint. Univ. Al I Cuza Iasi-Ser. Noua-Mat. 58 (2), 381-394, 2012.
  • [16] D.H. Jin and J.W. Lee, Generic lightlike submanifolds of an indefinite Kähler manifold, Int. J. Pure Appl. Math. 101 (4), 543–560, 2015.
  • [17] S.M. Khursheed Haider, M. Thakur and Advin, Screen Cauchy-Riemann lightlike submanifolds of a semi-Riemannian product manifold, Int. Electron. J. Geom. 4 (2), 141–154, 2011.
  • [18] E. Kılıç, B. Sahin and S. Keles, Screen semi-invariant lightlike submanifolds of a semi-Riemannian product manifolds, Int. Electron. J. Geom. 4 (2), 120–135, 2011.
  • [19] S. Kumar, R. Kumar and R.K. Nagaich, GCR-lightlike submanifolds of a semi- Riemannian product manifold, Bull. Korean Math. Soc. 51 (3), 883-899, 2014.
  • [20] N. (Önen) Poyraz, Golden GCR-lightlike submanifolds of golden semi-Riemannian manifolds, Mediterr. J. Math. 17 (5), 1-16, 2020.
  • [21] N. (Önen) Poyraz, A study on screen transversal lightlike submanifolds of golden semi-Riemannian manifolds, Facta Univ. Ser. Math. Inform. 36 (4), 717-733, 2021.
  • [22] X. Senlin and N. Yilong, Submanifolds of product Riemannian manifold, Acta Math. Sci. 20 (2), 213-218, 2000.
  • [23] B. Sahin, Screen transversal lightlike submanifolds of indefinite Kaehler manifolds, Chaos Solitons Fractals, 38, 1439–1448, 2008.
  • [24] C. Yıldırım and B. Sahin, Screen transversal lightlike submanifolds of indefinite Sasakian manifolds, Analele Stiint. Univ. Ovidius C. 18 (2), 315-336, 2010.
  • [25] C. Yıldırım and F.E. Erdogan, Radical screen transversal lightlike submanifolds of semi-Riemannian product manifolds, Math. Sci. Appl. E-Notes, 3 (1), 75-85, 2015.

Year 2024, Volume: 53 Issue: 1, 171 - 183, 29.02.2024

Nergiz Poyraz

https://doi.org/10.15672/hujms.1168604

Abstract

References

  • [1] M. Atçeken and E. Kılıç, Semi-invariant Lightlike submanifolds of a semi-Riemannian product manifold, Kodai. Math. J. 30 (3), 361-378, 2007.
  • [2] C.L. Bejan and K.L. Duggal, Global lightlike manifolds and harmonicity, Kodai. Math. J. 28, 131–145, 2005.
  • [3] B. Dogan, B. Sahin and E. Yasar, Screen generic lightlike submanifolds, Mediterr. J. Math. 16 (4), 21, 2019.
  • [4] K.L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and Its Applications, Kluwer Publisher, 1996.
  • [5] K.L. Duggal and B. Sahin, Screen cauchy Riemann lightlike submanifolds, Acta Math. Hung. 106 (1), 137-165, 2005.
  • [6] K.L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hung. 112 (1-2), 107–130, 2006.
  • [7] K.L. Duggal and B. Sahin, Lightlike submanifolds of indefinite Sasakian manifolds, Int. J. Math. Math. Sci. 2007, Art. No. 57585, 2007.
  • [8] K.L. Duggal and B. Sahin, Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Sasakian Manifolds, Acta Math. Hung. 122, 45–58, 2009.
  • [9] K.L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, 2010.
  • [10] F.E. Erdogan, On some types of lightlike submanifolds of golden semi-Riemannian manifolds, Filomat 33 (10), 3231-3242, 2019.
  • [11] F.E. Erdogan, S.Y. Perktas, B.E. Acet and A.M. Blaga, Screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds, J. Geom. Phys. 142, 111-120, 2019.
  • [12] R.S. Gupta and A. Sharfuddin, Generalized Cauchy-Riemann Lightlike Submanifolds of Indefinite Kenmotsu Manifolds, Note Mat. 30 (2), 49–59, 2010.
  • [13] R.S. Gupta, Screen Generic Lightlike Submanifolds of Indefinite Sasakian Manifolds, Mediterr. J. Math. 17 (5), 1-23, 2020.
  • [14] R.S. Gupta and A. Sharfuddin, Screen transversal lightlike submanifolds of indefinite cosymplectic manifolds, Rend. Semin. Mat. Univ. Padova, 124, 145-156, 2010.
  • [15] R.S. Gupta, A. Upadhyay and A. Sharfuddin, Generalised Cauchy-Riemann lightlike submanifolds of indefinite cosymplectic manifolds, Analele Stiint. Univ. Al I Cuza Iasi-Ser. Noua-Mat. 58 (2), 381-394, 2012.
  • [16] D.H. Jin and J.W. Lee, Generic lightlike submanifolds of an indefinite Kähler manifold, Int. J. Pure Appl. Math. 101 (4), 543–560, 2015.
  • [17] S.M. Khursheed Haider, M. Thakur and Advin, Screen Cauchy-Riemann lightlike submanifolds of a semi-Riemannian product manifold, Int. Electron. J. Geom. 4 (2), 141–154, 2011.
  • [18] E. Kılıç, B. Sahin and S. Keles, Screen semi-invariant lightlike submanifolds of a semi-Riemannian product manifolds, Int. Electron. J. Geom. 4 (2), 120–135, 2011.
  • [19] S. Kumar, R. Kumar and R.K. Nagaich, GCR-lightlike submanifolds of a semi- Riemannian product manifold, Bull. Korean Math. Soc. 51 (3), 883-899, 2014.
  • [20] N. (Önen) Poyraz, Golden GCR-lightlike submanifolds of golden semi-Riemannian manifolds, Mediterr. J. Math. 17 (5), 1-16, 2020.
  • [21] N. (Önen) Poyraz, A study on screen transversal lightlike submanifolds of golden semi-Riemannian manifolds, Facta Univ. Ser. Math. Inform. 36 (4), 717-733, 2021.
  • [22] X. Senlin and N. Yilong, Submanifolds of product Riemannian manifold, Acta Math. Sci. 20 (2), 213-218, 2000.
  • [23] B. Sahin, Screen transversal lightlike submanifolds of indefinite Kaehler manifolds, Chaos Solitons Fractals, 38, 1439–1448, 2008.
  • [24] C. Yıldırım and B. Sahin, Screen transversal lightlike submanifolds of indefinite Sasakian manifolds, Analele Stiint. Univ. Ovidius C. 18 (2), 315-336, 2010.
  • [25] C. Yıldırım and F.E. Erdogan, Radical screen transversal lightlike submanifolds of semi-Riemannian product manifolds, Math. Sci. Appl. E-Notes, 3 (1), 75-85, 2015.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Nergiz Poyraz 0000-0002-8110-712X

Early Pub Date August 15, 2023
Publication Date February 29, 2024
Published in Issue Year 2024 Volume: 53 Issue: 1

Cite

APA Poyraz, N. (2024). Screen generic lightlike submanifolds of semi-Riemannian product manifolds. Hacettepe Journal of Mathematics and Statistics, 53(1), 171-183. https://doi.org/10.15672/hujms.1168604
AMA Poyraz N. Screen generic lightlike submanifolds of semi-Riemannian product manifolds. Hacettepe Journal of Mathematics and Statistics. February 2024;53(1):171-183. doi:10.15672/hujms.1168604
Chicago Poyraz, Nergiz. “Screen Generic Lightlike Submanifolds of Semi-Riemannian Product Manifolds”. Hacettepe Journal of Mathematics and Statistics 53, no. 1 (February 2024): 171-83. https://doi.org/10.15672/hujms.1168604.
EndNote Poyraz N (February 1, 2024) Screen generic lightlike submanifolds of semi-Riemannian product manifolds. Hacettepe Journal of Mathematics and Statistics 53 1 171–183.
IEEE N. Poyraz, “Screen generic lightlike submanifolds of semi-Riemannian product manifolds”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 1, pp. 171–183, 2024, doi: 10.15672/hujms.1168604.
ISNAD Poyraz, Nergiz. “Screen Generic Lightlike Submanifolds of Semi-Riemannian Product Manifolds”. Hacettepe Journal of Mathematics and Statistics 53/1 (February 2024), 171-183. https://doi.org/10.15672/hujms.1168604.
JAMA Poyraz N. Screen generic lightlike submanifolds of semi-Riemannian product manifolds. Hacettepe Journal of Mathematics and Statistics. 2024;53:171–183.
MLA Poyraz, Nergiz. “Screen Generic Lightlike Submanifolds of Semi-Riemannian Product Manifolds”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 1, 2024, pp. 171-83, doi:10.15672/hujms.1168604.
Vancouver Poyraz N. Screen generic lightlike submanifolds of semi-Riemannian product manifolds. Hacettepe Journal of Mathematics and Statistics. 2024;53(1):171-83.

https://dergipark.org.tr/en/pub/hujms