On Lightlike Submanifolds of Poly-Norden Semi-Riemannian Manifolds

Year 2023, , 1 - 11, 30.06.2023

Erol Kılıç , Tuba Acet , Selcen Yüksel Perktaş

https://doi.org/10.47000/tjmcs.1110425

Abstract

In this paper, we introduce and examine invariant and semi-invariant lightlike submanifolds of a poly-Norden semi-Riemannian manifold. Also, we obtain some examples of such types submanifolds and study the conditions for both integrability and totally geodesic foliation description of distributions.

Keywords

Poly-Norden structure, lightlike submanifold, .

References

• Acet, B.E., Yüksel Perktaş, S., Kılıç, E., On lightlike geometry of para-Sasakian manifolds, Scientific Work J., Article ID 696231, (2014).
• Acet, B.E., Lightlike hypersurfaces of metallic semi-Riemannian manifolds, Int J Geo Meth in Modern Phys., 15(2018), 185–201.
• Acet, B.E., Screen pseudo slant lightlike submanifolds of golden semi-Riemannian manifolds, Hacettepe J Math and Stat., 49(2020), 2037–2045.
• Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and Its Applications, Kluwer Publisher, 1996.
• Duggal, K.L., Şahin, B., Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math Hungar., 112(2006), 107–130.
• Duggal, K.L., Şahin, B., Lightlike submanifolds of indefinite Sasakian manifolds, Int J Math and Math Sci., Article ID 57585, (2007).
• Duggal, K.L., Şahin, B., Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, 2010.
• Crasmareanu, M.C., Hretcanu, C.E., Golden differential geometry, Chaos, Solitons and Fractals, 38(2008), 1229–1238.
• Erdoğan, F.E., Transversal lightlike submanifolds of metallic semi-Riemannian manifolds, Turk J Math., 42(2018), 3133–3148.
• Erdoğan, F.E.,Yüksel Perktaş, S., Acet, B.E., Blaga, A.M., Screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds, J Geom Phys., 142(2019), 111–120.
• Galloway, G.J., Lecture notes on spacetime geometry, Beijing Int. Math. Research Center, (2007), 1–55.
• Gezer, A., Cengiz, N,Salimov, A., On integrability of golden Riemannian structure, Turk J Math., 37(2013), 693–703.
• Hretcanu, C.E., Crasmareanu, M.C., On some invariant submanifolds in a Riemannian manifold with golden structure, Analele Stiintifice Ale Universitatii Al.I. Cuza Iasi (N.S.), 53(2007), 199–211.
• Hretcanu, C.E., Crasmareanu, M.C., Metallic structure on Riemannian manifolds, Rev Un Mat Argen., 54(2013), 15–27.
• Hretcanu, C.E., Blaga, A.M., Submanifolds in metallic semi-Riemannian manifolds, Differ Geom Dynm Syst., 20(2018), 83–97.
• Kalia, S., The generalizations of the golden ratio, their powers, continued fractions and convergents, http://math.mit.edu/research/highschool/primes/papers.php.
• Önen Poyraz, N., Yaşar, E., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediter J Math., 14(2017), 1–20.
• Spinadel, V.W., The metallic means family and forbidden symmetries, Int Math J., 2(2002), 279–288.
• Şahin, B., Almost poly-Norden manifolds, Int J Maps Math., 1(2018), 68–79.
• Yüksel Perktasş, S., Erdoğan, F.E., On generalized CR-lightlike submanifolds, Palestine J Math., 8(2019), 200–208.
• Yüksel Perktaş, S., Submanifolds of almost poly-Norden Riemannian manifolds, Turk J Math., 44(2020), 31–49.