Araştırma Makalesi
BibTex RIS Kaynak Göster

Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds

Yıl 2020, Cilt: 22 Sayı: 1, 106 - 121, 10.01.2020
https://doi.org/10.25092/baunfbed.679537

Öz

In this study, we introduce semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. We find some conditions for integrability of distributions. Morever, we investigate totally geodesic and mixed geodesic distributions of such a submanifold. The paper also contains an example.

Kaynakça

  • Acet, B. E., Lightlike hypersurfaces of metallic semi-Riemannian manifolds, Int. Jour. of Geometric method in modern Physics, 15(12), 185-201, (2018).
  • Acet, B. E., Perktaş, S. Y. and Kılıç, E., Lightlike Submanifolds of a Para-Sasakian Manifold, Gen. Math. Notes, 22(2), 22-45, (2014).
  • Atçeken, M. and Kılıç, E., Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold, Kodai Math. J., 30(3), 361-378, (2007).
  • Bahadır, O. and Kılıç, E., Lightlike submanifolds of indefinite Kaehler manifolds with quarter symmetric non-metric connection, Mathematical Sciences And Applications E-Notes, 2(2), 89-104, (2014).
  • Bahadır, O. and Kılıç, E., Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection, International Electronic Journal of Geometry, 9(1), 9-22, (2016).
  • Crasmareanu, M. and Hretcanu, C. E., Golden Differential Geometry, Chaos, Solitons & Fractals, 38, 1229-1238, (2008).
  • Duggal, K. L. and Bejancu, A., Lightlike submanifold of semi-Riemannian manifolds and its applications, Kluwer Academic, The Netherlands, (1996).
  • Duggal, K. L. and Şahin, B., Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 106(1-2), 137-165, (2005).
  • Duggal, K. L. and Şahin, B., Generalized Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 112(1-2), 113-136, (2006).
  • Duggal, K. L. and Şahin, B., Differential geometry of lightlike submanifolds, Birkhäuser Verlag, (2010).
  • Erdoğan, F. E., Transversal lightlike submanifolds of metallic semi-Riemannian manifolds, Turkish Journal of Mathematics, 42 (6), 3133-3148, (2018).
  • Erdoğan, F. E. and Yıldırım, C., On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds, Politeknik Dergisi 21 (4), 967-970, (2018).
  • Gezer, A., Cengiz, N., Salimov, A., On integrability of golden Riemannian structures, Turk. J. Math., 37, 693-703, (2013).
  • Goldberg S.I., Yano K., Polynomial structures on manifolds, Kodai Math. Sem. Rep., 22, 199-218, (1970).
  • 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, suppl. 1, 199-211, (2007).
  • Kılıç, E. and Şahin, B., Radical anti-invariant lightlike submanifolds of a Semi-Riemannian Product Manifold, Turkish Journal of Mathematics, 32, 429-449, (2008).
  • Kupeli, D. N., Singular Semi-Riemannian Geometry, Kluwer Academic Publishers, Dordrecht, (1996).
  • Özkan, M., Prolongations of golden structures to tangent bundles, Diff. Geom. Dyn. Syst., 16, 227-238, (2014).
  • (Önen) Poyraz, N. and Yaşar, E., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediterr. J. Math., 14:204, (2017).
  • Yano, K., On a structure defined by a tensor field of type (1,1) satisfying, Tensor, N.S., 14, 99-109, (1963).
  • Yano, K. and Kon, M., Structure on manifolds, World Scientific Publishing, (1984).

Altın semi-Riemann manifoldların semi-invaryant lightlike altmanifoldları

Yıl 2020, Cilt: 22 Sayı: 1, 106 - 121, 10.01.2020
https://doi.org/10.25092/baunfbed.679537

Öz

Bu makalede altın semi-Riemann manifoldların semi-invaryant lightlike altmanifoldlarını çalıştık. Distribüsyonların integrallenebilirliği için bazı koşullar bulduk. Ayrıca, böyle bir altmanifoldun tamamen geodezik ve mixed geodezik distribüsyonlarını inceledik. Makale, bir adet örnek içermektedir.

Kaynakça

  • Acet, B. E., Lightlike hypersurfaces of metallic semi-Riemannian manifolds, Int. Jour. of Geometric method in modern Physics, 15(12), 185-201, (2018).
  • Acet, B. E., Perktaş, S. Y. and Kılıç, E., Lightlike Submanifolds of a Para-Sasakian Manifold, Gen. Math. Notes, 22(2), 22-45, (2014).
  • Atçeken, M. and Kılıç, E., Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold, Kodai Math. J., 30(3), 361-378, (2007).
  • Bahadır, O. and Kılıç, E., Lightlike submanifolds of indefinite Kaehler manifolds with quarter symmetric non-metric connection, Mathematical Sciences And Applications E-Notes, 2(2), 89-104, (2014).
  • Bahadır, O. and Kılıç, E., Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection, International Electronic Journal of Geometry, 9(1), 9-22, (2016).
  • Crasmareanu, M. and Hretcanu, C. E., Golden Differential Geometry, Chaos, Solitons & Fractals, 38, 1229-1238, (2008).
  • Duggal, K. L. and Bejancu, A., Lightlike submanifold of semi-Riemannian manifolds and its applications, Kluwer Academic, The Netherlands, (1996).
  • Duggal, K. L. and Şahin, B., Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 106(1-2), 137-165, (2005).
  • Duggal, K. L. and Şahin, B., Generalized Cauchy Riemann lightlike submanifolds, Acta Math. Hungar., 112(1-2), 113-136, (2006).
  • Duggal, K. L. and Şahin, B., Differential geometry of lightlike submanifolds, Birkhäuser Verlag, (2010).
  • Erdoğan, F. E., Transversal lightlike submanifolds of metallic semi-Riemannian manifolds, Turkish Journal of Mathematics, 42 (6), 3133-3148, (2018).
  • Erdoğan, F. E. and Yıldırım, C., On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds, Politeknik Dergisi 21 (4), 967-970, (2018).
  • Gezer, A., Cengiz, N., Salimov, A., On integrability of golden Riemannian structures, Turk. J. Math., 37, 693-703, (2013).
  • Goldberg S.I., Yano K., Polynomial structures on manifolds, Kodai Math. Sem. Rep., 22, 199-218, (1970).
  • 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, suppl. 1, 199-211, (2007).
  • Kılıç, E. and Şahin, B., Radical anti-invariant lightlike submanifolds of a Semi-Riemannian Product Manifold, Turkish Journal of Mathematics, 32, 429-449, (2008).
  • Kupeli, D. N., Singular Semi-Riemannian Geometry, Kluwer Academic Publishers, Dordrecht, (1996).
  • Özkan, M., Prolongations of golden structures to tangent bundles, Diff. Geom. Dyn. Syst., 16, 227-238, (2014).
  • (Önen) Poyraz, N. and Yaşar, E., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediterr. J. Math., 14:204, (2017).
  • Yano, K., On a structure defined by a tensor field of type (1,1) satisfying, Tensor, N.S., 14, 99-109, (1963).
  • Yano, K. and Kon, M., Structure on manifolds, World Scientific Publishing, (1984).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Nergiz (önen) Poyraz 0000-0002-8110-712X

Burçin Doğan Bu kişi benim 0000-0001-8386-213X

Yayımlanma Tarihi 10 Ocak 2020
Gönderilme Tarihi 8 Mart 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 22 Sayı: 1

Kaynak Göster

APA (önen) Poyraz, N., & Doğan, B. (2020). Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(1), 106-121. https://doi.org/10.25092/baunfbed.679537
AMA (önen) Poyraz N, Doğan B. Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. BAUN Fen. Bil. Enst. Dergisi. Ocak 2020;22(1):106-121. doi:10.25092/baunfbed.679537
Chicago (önen) Poyraz, Nergiz, ve Burçin Doğan. “Semi-Invariant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, sy. 1 (Ocak 2020): 106-21. https://doi.org/10.25092/baunfbed.679537.
EndNote (önen) Poyraz N, Doğan B (01 Ocak 2020) Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 1 106–121.
IEEE N. (önen) Poyraz ve B. Doğan, “Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds”, BAUN Fen. Bil. Enst. Dergisi, c. 22, sy. 1, ss. 106–121, 2020, doi: 10.25092/baunfbed.679537.
ISNAD (önen) Poyraz, Nergiz - Doğan, Burçin. “Semi-Invariant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/1 (Ocak 2020), 106-121. https://doi.org/10.25092/baunfbed.679537.
JAMA (önen) Poyraz N, Doğan B. Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. BAUN Fen. Bil. Enst. Dergisi. 2020;22:106–121.
MLA (önen) Poyraz, Nergiz ve Burçin Doğan. “Semi-Invariant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 22, sy. 1, 2020, ss. 106-21, doi:10.25092/baunfbed.679537.
Vancouver (önen) Poyraz N, Doğan B. Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds. BAUN Fen. Bil. Enst. Dergisi. 2020;22(1):106-21.