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.