On Lightlike Submanifolds of Poly-Norden Semi-Riemannian Manifolds

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

1. Acet, B.E., Yüksel Perktaş, S., Kılıç, E., On lightlike geometry of para-Sasakian manifolds, Scientific Work J., Article ID 696231, (2014).
2. Acet, B.E., Lightlike hypersurfaces of metallic semi-Riemannian manifolds, Int J Geo Meth in Modern Phys., 15(2018), 185–201.
3. Acet, B.E., Screen pseudo slant lightlike submanifolds of golden semi-Riemannian manifolds, Hacettepe J Math and Stat., 49(2020), 2037–2045.
4. Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and Its Applications, Kluwer Publisher, 1996.
5. Duggal, K.L., Şahin, B., Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math Hungar., 112(2006), 107–130.
6. Duggal, K.L., Şahin, B., Lightlike submanifolds of indefinite Sasakian manifolds, Int J Math and Math Sci., Article ID 57585, (2007).
7. Duggal, K.L., Şahin, B., Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, 2010.
8. Crasmareanu, M.C., Hretcanu, C.E., Golden differential geometry, Chaos, Solitons and Fractals, 38(2008), 1229–1238.

9. Erdoğan, F.E., Transversal lightlike submanifolds of metallic semi-Riemannian manifolds, Turk J Math., 42(2018), 3133–3148.
10. 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.
11. Galloway, G.J., Lecture notes on spacetime geometry, Beijing Int. Math. Research Center, (2007), 1–55.
12. Gezer, A., Cengiz, N,Salimov, A., On integrability of golden Riemannian structure, Turk J Math., 37(2013), 693–703.
13. 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.
14. Hretcanu, C.E., Crasmareanu, M.C., Metallic structure on Riemannian manifolds, Rev Un Mat Argen., 54(2013), 15–27.
15. Hretcanu, C.E., Blaga, A.M., Submanifolds in metallic semi-Riemannian manifolds, Differ Geom Dynm Syst., 20(2018), 83–97.
16. Kalia, S., The generalizations of the golden ratio, their powers, continued fractions and convergents, http://math.mit.edu/research/highschool/primes/papers.php.
17. Önen Poyraz, N., Yaşar, E., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediter J Math., 14(2017), 1–20.
18. Spinadel, V.W., The metallic means family and forbidden symmetries, Int Math J., 2(2002), 279–288.
19. Şahin, B., Almost poly-Norden manifolds, Int J Maps Math., 1(2018), 68–79.
20. Yüksel Perktasş, S., Erdoğan, F.E., On generalized CR-lightlike submanifolds, Palestine J Math., 8(2019), 200–208.
21. Yüksel Perktaş, S., Submanifolds of almost poly-Norden Riemannian manifolds, Turk J Math., 44(2020), 31–49.