Year 2020,
Volume: 3 Issue: 2, 121 - 130, 31.07.2020
Nergiz (önen) Poyraz
,
Burçin Doğan
References
- Acet, B. E., Perktaş, S. Y. and Kılıç, E., Lightlike Submanifolds of a Para-Sasakian Manifold, Gen. Math. Notes, Vol. 22, No. 2, (2014), pp. 22-45.
- Atçeken, M. and Kiliç, E. Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold. Kodai Math. J. Vol. 30, No. 3, (2007), pp. 361-378. Bahadır, O. and Kılıç, E., Lightlike Submanifolds of Indefinite Kaehler Manifolds with Quarter Symmetric Non-Metric Connection, Mathematical Sciences And Applications E-Notes, Volume 2, No. 2, (2014), pp. 89-104.
- 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), (2016), 9-22.
- Crasmareanu, M. and Hretcanu, C. E., Golden Differential Geometry, Chaos, Solitons and Fractals, 38, (2008), 1229-1238.
- Duggal, K. L. and Bejancu, A., Lightlike Submanifold of Semi-Riemannian Manifolds and Applications, Kluwer Academic Pub., The Netherlands, 1996.
- Duggal, K. L. and Şahin, B., Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hungar., 106 (1-2), (2005), 137-165.
- Duggal, K. L. and Sahin, B., Generalized Cauchy Riemann lightlike submanifolds. Acta Math. Hungar., 112 (1-2), (2006), 113-136.
- Duggal, K. L. and Şahin, B., Differential Geometry of Lightlike Submanifolds, Birkhäuser Verlag AG., 2010.
- Gezer, A., Cengiz, N., Salimov, A., On integrability of Golden Riemannian structures, Turk J. Math., 37, (2013), 693-703. Goldberg S.I., Yano K., Polynomial structures on manifolds. Kodai Math. Sem. Rep., 22, (1970), 199-218.
- 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 (2007), suppl. 1, 199-211.
- Hretcanu, C. E., Crasmareanu, M., Applications of the golden ratio on Riemannian manifolds, Tübitak, Turk. J. Math., 33, (2009), 179-191.
- Kılıç,, E. and Şahin, B., Radical Anti-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold, Turkish J. Math., 32, (2008), 429-449.
- 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, (2014), 227-238. (Önen) Poyraz N. and Yaşar E., Lightlike Hypersurfaces of A Golden Semi-Riemannian Manifold, Mediterr. J. Math., (2017), 14:204.
- Yano, K. and Kon, M., Structure on manifolds, World Scientific Publishing Co.Ltd., 1984.
- Yano, K., On a structure defined by a tensor field f of type (1,1) satisfying f³+f=0, Tensor, N.S., 14, (1963), 99-109.
GEOMETRY OF SEMI-INVARIANT COISOTROPIC SUBMANIFOLDS IN GOLDEN SEMI-RIEMANNIAN MANIFOLDS
Year 2020,
Volume: 3 Issue: 2, 121 - 130, 31.07.2020
Nergiz (önen) Poyraz
,
Burçin Doğan
Abstract
In this paper, we study semi-invariant coisotropic lightlike submanifolds of a golden semi-Riemannian manifold. We give some necessary and sufficient conditions on integrability of distibutions on semi-invariant coisotropic lightlike submanifolds of a golden semi-Riemannian manifold. We obtain some geometric results for coisotropic lightlike submanifolds of a golden semi-Riemannian manifold. Moreover, we give an example.
References
- Acet, B. E., Perktaş, S. Y. and Kılıç, E., Lightlike Submanifolds of a Para-Sasakian Manifold, Gen. Math. Notes, Vol. 22, No. 2, (2014), pp. 22-45.
- Atçeken, M. and Kiliç, E. Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold. Kodai Math. J. Vol. 30, No. 3, (2007), pp. 361-378. Bahadır, O. and Kılıç, E., Lightlike Submanifolds of Indefinite Kaehler Manifolds with Quarter Symmetric Non-Metric Connection, Mathematical Sciences And Applications E-Notes, Volume 2, No. 2, (2014), pp. 89-104.
- 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), (2016), 9-22.
- Crasmareanu, M. and Hretcanu, C. E., Golden Differential Geometry, Chaos, Solitons and Fractals, 38, (2008), 1229-1238.
- Duggal, K. L. and Bejancu, A., Lightlike Submanifold of Semi-Riemannian Manifolds and Applications, Kluwer Academic Pub., The Netherlands, 1996.
- Duggal, K. L. and Şahin, B., Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hungar., 106 (1-2), (2005), 137-165.
- Duggal, K. L. and Sahin, B., Generalized Cauchy Riemann lightlike submanifolds. Acta Math. Hungar., 112 (1-2), (2006), 113-136.
- Duggal, K. L. and Şahin, B., Differential Geometry of Lightlike Submanifolds, Birkhäuser Verlag AG., 2010.
- Gezer, A., Cengiz, N., Salimov, A., On integrability of Golden Riemannian structures, Turk J. Math., 37, (2013), 693-703. Goldberg S.I., Yano K., Polynomial structures on manifolds. Kodai Math. Sem. Rep., 22, (1970), 199-218.
- 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 (2007), suppl. 1, 199-211.
- Hretcanu, C. E., Crasmareanu, M., Applications of the golden ratio on Riemannian manifolds, Tübitak, Turk. J. Math., 33, (2009), 179-191.
- Kılıç,, E. and Şahin, B., Radical Anti-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold, Turkish J. Math., 32, (2008), 429-449.
- 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, (2014), 227-238. (Önen) Poyraz N. and Yaşar E., Lightlike Hypersurfaces of A Golden Semi-Riemannian Manifold, Mediterr. J. Math., (2017), 14:204.
- Yano, K. and Kon, M., Structure on manifolds, World Scientific Publishing Co.Ltd., 1984.
- Yano, K., On a structure defined by a tensor field f of type (1,1) satisfying f³+f=0, Tensor, N.S., 14, (1963), 99-109.