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
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
Nergiz (önen) Poyraz
,
Burçin Doğan
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).