Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds

Abstract

In this article, we initiate the study of lightlike hypersurfaces in a poly-Norden semi-Riemannian manifold. We introduce invariant and screen semi-invariant lightlike hypersurfaces of a poly-Norden semi- Riemannian manifold. Also, we give some examples of such hypersurfaces.

Keywords

• Almost poly-Norden structure
• poly-Norden manifold
• Lightlike hypersurface

Kaynakça

1. [1] Duggal KL, Bejancu A. Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications. Kluwer Publisher, 1996.
2. [2] Duggal KL, Şahin B. Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. Acta Math Hungarica. 112, 2006, 107 -– 130.
3. [3] Duggal KL, Şahin B. Lightlike submanifolds of indefinite Sasakian manifolds. Int J Math and Math Sci. Article ID 57585, 2007.
4. [4] Duggal KL, Şahin B. Differential geometry of lightlike submanifolds. Frontiers in Mathematics, 2010.
5. [5] Galloway GJ. Lecture notes on spacetime geometry. Beijing Int. Math. Research Center. 1-55, 2007.
6. [6] Acet BE, Yüksel Perktaş S, Kılıç, E. Symmetric lightlike hypersurfaces of a para-Sasakian space form. Analele Stiintifice Ale Universitatii Al.I. Cuza Iasi (N.S.) 2, 2016, 915 -– 926.
7. [7] Acet BE, Yüksel Perktas¸ S, Kılıç, E. On lightlike geometry of para-Sasakian manifolds. Scientific Work J. Article ID 696231, 2014.
8. [8] Yüksel Perktas¸ S, Erdoğan FE. On generalized CR-lightlike submanifolds. Palestine J Math. 8(1), 2019, 200 -– 208.

9. [9] Crasmareanu MC, Hretcanu CE. Golden differential geometry. Chaos, Solitons and Fractals. 38(5), 2008, 1229 -– 1238.
10. [10] Hretcanu CE, Crasmareanu MC. On some invariant submanifolds in a Riemannian manifold with golden structure. Analele Stiintifice Ale Universitatii Al.I. Cuza Iasi (N.S.) 53(1), 2007, 199 -– 211.
11. [11] Gezer A, Cengiz N, Salimov A. On integrability of golden Riemannian structure. Turk J Math. 37, 2013, 693 -– 703.
12. [12] Erdoğan FE, Yıldırım C. n a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds. J Polytech. 21(4), 2018, 967 -– 970.
13. [13] Ö nen Poyraz N, Yaşar E. Lightlike hypersurfaces of a golden semi-Riemannian manifold. Mediter J Math. 14(204), 2017, 1 -– 20.
14. [14] Spinadel VW. he metallic means family and forbidden symmetries. Int Math J. 2(3), 2002, 279 -– 288.
15. [15] Acet BE. Lightlike hypersurfaces of metallic semi-Riemannian manifolds. Int J Geo Meth in Modern Phys. 15(12), 2018, 185 -– 201.
16. [16] Erdoğan FE. Transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Turk J Math. 42, 2018, 3133 -– 3148.
17. [17] Hretcanu CE, Blaga AM. Submanifolds in metallic semi-Riemannian manifolds. Differ Geom Dynm Syst. 20, 2018, 83 -– 97.
18. [18] Erdoğan FE,Y üksel Perktas¸ S, Acet BE. Blaga AM. Screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds. J Geom Phys. 142, 2019, 111 -– 120.
19. [19] Kalia S. The generalizations of the golden ratio, their powers, continued fractions and convergents, http://math.mit.edu/research/highschool/primes/papers.php
20. [20] Hretcanu CE, Crasmareanu MC. Metallic structure on Riemannian manifolds. Rev Un Mat Argentina. 54(2), 2013, 15 -– 27.
21. [21] Şahin B. Almost poly-Norden manifolds. Int J Maps in Math. 1(1), 2018, 68 -– 79.
22. [22] Yüksel Perktas¸ S. Submanifolds of almost poly-Norden Riemannian manifolds. Turk J Math. 44(1), 2020, 31 -– 49.