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Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds

Year 2022, Volume: 7 Issue: 1, 21 - 30, 30.04.2022

Erol Kılıç Tuba Acet Selcen Yüksel Perktaş

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

References

  • [1] Duggal KL, Bejancu A. Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications. Kluwer Publisher, 1996.
  • [2] Duggal KL, Şahin B. Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. Acta Math Hungarica. 112, 2006, 107 -– 130.
  • [3] Duggal KL, Şahin B. Lightlike submanifolds of indefinite Sasakian manifolds. Int J Math and Math Sci. Article ID 57585, 2007.
  • [4] Duggal KL, Şahin B. Differential geometry of lightlike submanifolds. Frontiers in Mathematics, 2010.
  • [5] Galloway GJ. Lecture notes on spacetime geometry. Beijing Int. Math. Research Center. 1-55, 2007.
  • [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] Acet BE, Yüksel Perktas¸ S, Kılıç, E. On lightlike geometry of para-Sasakian manifolds. Scientific Work J. Article ID 696231, 2014.
  • [8] Yüksel Perktas¸ S, Erdoğan FE. On generalized CR-lightlike submanifolds. Palestine J Math. 8(1), 2019, 200 -– 208.
  • [9] Crasmareanu MC, Hretcanu CE. Golden differential geometry. Chaos, Solitons and Fractals. 38(5), 2008, 1229 -– 1238.
  • [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] Gezer A, Cengiz N, Salimov A. On integrability of golden Riemannian structure. Turk J Math. 37, 2013, 693 -– 703.
  • [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] Ö nen Poyraz N, Yaşar E. Lightlike hypersurfaces of a golden semi-Riemannian manifold. Mediter J Math. 14(204), 2017, 1 -– 20.
  • [14] Spinadel VW. he metallic means family and forbidden symmetries. Int Math J. 2(3), 2002, 279 -– 288.
  • [15] Acet BE. Lightlike hypersurfaces of metallic semi-Riemannian manifolds. Int J Geo Meth in Modern Phys. 15(12), 2018, 185 -– 201.
  • [16] Erdoğan FE. Transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Turk J Math. 42, 2018, 3133 -– 3148.
  • [17] Hretcanu CE, Blaga AM. Submanifolds in metallic semi-Riemannian manifolds. Differ Geom Dynm Syst. 20, 2018, 83 -– 97.
  • [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] Kalia S. The generalizations of the golden ratio, their powers, continued fractions and convergents, http://math.mit.edu/research/highschool/primes/papers.php
  • [20] Hretcanu CE, Crasmareanu MC. Metallic structure on Riemannian manifolds. Rev Un Mat Argentina. 54(2), 2013, 15 -– 27.
  • [21] Şahin B. Almost poly-Norden manifolds. Int J Maps in Math. 1(1), 2018, 68 -– 79.
  • [22] Yüksel Perktas¸ S. Submanifolds of almost poly-Norden Riemannian manifolds. Turk J Math. 44(1), 2020, 31 -– 49.

Year 2022, Volume: 7 Issue: 1, 21 - 30, 30.04.2022

Erol Kılıç Tuba Acet Selcen Yüksel Perktaş

Abstract

References

  • [1] Duggal KL, Bejancu A. Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications. Kluwer Publisher, 1996.
  • [2] Duggal KL, Şahin B. Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. Acta Math Hungarica. 112, 2006, 107 -– 130.
  • [3] Duggal KL, Şahin B. Lightlike submanifolds of indefinite Sasakian manifolds. Int J Math and Math Sci. Article ID 57585, 2007.
  • [4] Duggal KL, Şahin B. Differential geometry of lightlike submanifolds. Frontiers in Mathematics, 2010.
  • [5] Galloway GJ. Lecture notes on spacetime geometry. Beijing Int. Math. Research Center. 1-55, 2007.
  • [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] Acet BE, Yüksel Perktas¸ S, Kılıç, E. On lightlike geometry of para-Sasakian manifolds. Scientific Work J. Article ID 696231, 2014.
  • [8] Yüksel Perktas¸ S, Erdoğan FE. On generalized CR-lightlike submanifolds. Palestine J Math. 8(1), 2019, 200 -– 208.
  • [9] Crasmareanu MC, Hretcanu CE. Golden differential geometry. Chaos, Solitons and Fractals. 38(5), 2008, 1229 -– 1238.
  • [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] Gezer A, Cengiz N, Salimov A. On integrability of golden Riemannian structure. Turk J Math. 37, 2013, 693 -– 703.
  • [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] Ö nen Poyraz N, Yaşar E. Lightlike hypersurfaces of a golden semi-Riemannian manifold. Mediter J Math. 14(204), 2017, 1 -– 20.
  • [14] Spinadel VW. he metallic means family and forbidden symmetries. Int Math J. 2(3), 2002, 279 -– 288.
  • [15] Acet BE. Lightlike hypersurfaces of metallic semi-Riemannian manifolds. Int J Geo Meth in Modern Phys. 15(12), 2018, 185 -– 201.
  • [16] Erdoğan FE. Transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Turk J Math. 42, 2018, 3133 -– 3148.
  • [17] Hretcanu CE, Blaga AM. Submanifolds in metallic semi-Riemannian manifolds. Differ Geom Dynm Syst. 20, 2018, 83 -– 97.
  • [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] Kalia S. The generalizations of the golden ratio, their powers, continued fractions and convergents, http://math.mit.edu/research/highschool/primes/papers.php
  • [20] Hretcanu CE, Crasmareanu MC. Metallic structure on Riemannian manifolds. Rev Un Mat Argentina. 54(2), 2013, 15 -– 27.
  • [21] Şahin B. Almost poly-Norden manifolds. Int J Maps in Math. 1(1), 2018, 68 -– 79.
  • [22] Yüksel Perktas¸ S. Submanifolds of almost poly-Norden Riemannian manifolds. Turk J Math. 44(1), 2020, 31 -– 49.
There are 22 citations in total.

Details

Primary Language English
Journal Section Volume VII Issue I
Authors

Erol Kılıç 0000-0001-7536-0404

Tuba Acet 0000-0002-5096-3388

Selcen Yüksel Perktaş 0000-0002-8848-0621

Publication Date April 30, 2022
Published in Issue Year 2022 Volume: 7 Issue: 1

Cite

APA Kılıç, E., Acet, T., & Yüksel Perktaş, S. (2022). Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds. Turkish Journal of Science, 7(1), 21-30.
AMA Kılıç E, Acet T, Yüksel Perktaş S. Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds. TJOS. April 2022;7(1):21-30.
Chicago Kılıç, Erol, Tuba Acet, and Selcen Yüksel Perktaş. “Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds”. Turkish Journal of Science 7, no. 1 (April 2022): 21-30.
EndNote Kılıç E, Acet T, Yüksel Perktaş S (April 1, 2022) Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds. Turkish Journal of Science 7 1 21–30.
IEEE E. Kılıç, T. Acet, and S. Yüksel Perktaş, “Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds”, TJOS, vol. 7, no. 1, pp. 21–30, 2022.
ISNAD Kılıç, Erol et al. “Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds”. Turkish Journal of Science 7/1 (April 2022), 21-30.
JAMA Kılıç E, Acet T, Yüksel Perktaş S. Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds. TJOS. 2022;7:21–30.
MLA Kılıç, Erol et al. “Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds”. Turkish Journal of Science, vol. 7, no. 1, 2022, pp. 21-30.
Vancouver Kılıç E, Acet T, Yüksel Perktaş S. Lightlike Hypersurfaces of Poly-Norden Semi-Riemannian Manifolds. TJOS. 2022;7(1):21-30.
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