Semi-invariant lightlike submanifolds of golden semi-Riemannian manifolds

Yıl 2020, Cilt: 22 Sayı: 1, 106 - 121, 10.01.2020

Nergiz (önen) Poyraz Burçin Doğan

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.

Anahtar Kelimeler

Lightlike submanifold, Golden semi-Riemann manifold, semi-invariant submanifold

Altın semi-Riemann manifoldların semi-invaryant lightlike altmanifoldları

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.

Anahtar Kelimeler

Lightlike altmanifold, Altın semi-Riemann manifold, semi-invaryant altmanifold

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).