Screen Semi-Invariant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds

Yıl 2021, Cilt: 14 Sayı: 1, 207 - 216, 15.04.2021

Nergiz Poyraz

https://doi.org/10.36890/iejg.893398

Cited By: 5

Öz

In this paper, we present screen semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. We research several properties of such submanifolds and get the conditions of integrability of distributions. We prove some results for totally umbilical screen semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. We also give an example.

Anahtar Kelimeler

Golden semi-Riemannian manifolds, golden structure, lightlike submanifolds, screen semi-invariant lightlike submanifolds

Kaynakça

• [1] Acet, B. E., Perktaş, S. Y., Kılıç, E.: Lightlike Submanifolds of a Para-Sasakian Manifold. General Mathematics Notes. 22(2), 22-45 (2014).
• [2] Acet, B. E.: Screen pseudo slant lightlike submanifolds of golden semi-Riemannian manifolds. Hacet. J. Math. Stat. 49(6), 2037-2045 (2020).
• [3] Crasmareanu, M., Hretcanu, C. E.: Golden Differential Geometry. Chaos, Solitons and Fractals. 38, 1229-1238 (2008).
• [4] Do˘gan, B., .Şahin, B., Ya¸sar, E.: Screen Transversal Cauchy Riemann Lightlike Submanifolds. Filomat. 34(5), 1581-1599 (2020).
• [5] Do˘gan, B., Şahin, B., Ya¸sar, E.: Screen Generic Lightlike Submanifolds. Mediterr. J. Math. 16, 104, (2019).
• [6] Duggal, K. L., Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic Pub., The Netherlands (1996).
• [7] Duggal, K. L., Jin, D. H.: Totally Umbilical Lightlike Submanifolds. Kodai Math. J. 26(1), 49-68 (2003).
• [8] Duggal, K. L., Şahin, B.: Screen Cauchy-Riemann lightlike submanifolds. Acta Math. Hungar. 106(1-2), 137–165 (2005).
• [9] Duggal, K. L., Şahin, B.: Differential Geometry of Lightlike Submanifolds. Birkhäuser Verlag AG, Basel, Boston, Berlin (2010).
• [10] Erdoğan, F. E., Yildirim, C.: On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds. Politeknik Dergisi. 21(4), 967-970 (2018).
• [11] Gök, M., Keleş S., Kılıç, E.: Schouten and Vr˘anceanu Connections on Golden Manifolds. Int. Electron. J. Geom. 12(2), 169-181 (2019).
• [12] Hretcanu, C.E.: Submanifolds in Riemannian manifold with golden structure. Workshop on Finsler Geometry and its Applications. Hungary (2007).
• [13] Hretcanu, C. E., Crasmareanu, M.: On some invariant submanifolds in Riemannian manifold with Golden Structure. An. Ştiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 53(1), 199–211 (2007).
• [14] Hretcanu, C. E., Crasmareanu, M.: Applications of the golden ratio on Riemannian manifolds. Turkish J. Math. 33(2), 179-191 (2009).
• [15] Khursheed Haider, S. M., Thakur, M., Advin: Screen Cauchy-Riemann lightlike submanifolds of a semi-Riemannian product manifold. Int. Electron. J. Geom. 4(2), 141–154 (2011).
• [16] Kılıç, E., Şahin, B.: Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds. Turkish J. Math. 32(4), 429-449 (2008).
• [17] Kılıç, E., Şahin, B., Keleş, S.: Screen semi-invariant lightlike submanifolds of a semi-Riemannian product manifolds. Int. Electron. J. Geom. 4(2), 120–135 (2011).
• [18] Kumar, R., Rani, R., Nagaich, R.K.: Some properties of lightlike submanifolds of semi-Riemannian manifolds. Demonstr. Math. 43(5), 691-701 (2010).
• [19] Özkan, M.: Prolongations of golden structures to tangent bundles. Diff. Geom. Dyn. Syst. 16, 227-238 (2014).
• [20] (Önen) Poyraz, N., Ya¸sar, E.: Lightlike submanifolds of golden semi–Riemannian manifolds. J. Geom. Phys. 141, 92-104 (2019).
• [21] ¸Sahin, B., Akyol, M. A.: Golden maps between Golden Riemannian manifolds and constancy of certain maps. Math. Commun. 19(2), 333-342 (2014).
• [22] Yücesan, A., Yaşar, E.: Lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Bull. Korean Math. Soc. 47(5), 1089-1103 (2010).