PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r
Year 2016,
Volume: 65 Issue: 1, 35 - 48, 01.02.2016
Mustafa Özkan
Fatma Yılmaz
Abstract
Our purpose in this paper is to focus on some applications in differential geometry of golden structure. We study rlift of the golden structure
in tangent bundle of order r and we obtain integrabilitiy conditions of golden
structure in TrM
References
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- Crasmareanu, M., Hretcanu, C.E., Golden diğerential geometry, Chaos, Solitons and Fractals (2008), 1229-1238.
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- Hretcanu, C.E., Crasmareanu, M., On some invariant submanifolds in a Riemannian manifold with golden structure, An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 53(1) (2007), 199-211.
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- Morimoto, A., Liftings of tensor …elds and connections to tangent bundles of higher order, Nagoya Math. J. 40 (1970), 99-120.
- Omran, T., Sharğuddin, A., Husain, S.I., Lifts of structures on manifolds, Publications De L’institut Math. 36, 50 (1984), 93-97.
- Özdemir, F., Crasmareanu, M., Geometrical ob jects associated to a substructure, Turk J. Math. 34 (2010), 1-12.
- Özkan, M., Prolongations of golden structures to tangent bundles, Diğer. Geom. Dyn. Syst. (2014), 227-238.
- Pripoae, G.T., Classi…cation of semi-Riemannian almost product structure, BSG Proc. 11, Geometry Balkan Press, Bucharest (2004), 243-251.
- ¸Sahin, B., Akyol, M.A., Golden maps between Golden Riemannian manifolds and constancy of certain maps, Math. Commun. 19 (2014), 1-10.
- Yardımcı, E.H., Yaylı, Y., Golden quaternionic structures, Int. Electron. J. Pure Appl. Math. (2014), 109-125.
- Yano, K., Ishihara, S., Tangent and cotangent bundle, 1973, New York: Marcel Dekker Inc.
- Current address, M. Özkan: Gazi University, Faculty of Science, Department of Mathematics, , Teknikokullar / Ankara - Turkey E-mail address, M. Özkan: ozkanm@gazi.edu.tr Current address, F. Yılmaz: Gazi University, Faculty of Science, Department of Mathematics, , Teknikokullar / Ankara - Turkey E-mail address, F. Yılmaz: fatmayilmaz@gazi.edu.tr
Year 2016,
Volume: 65 Issue: 1, 35 - 48, 01.02.2016
Mustafa Özkan
Fatma Yılmaz
References
- Cordero, L.A., The extension of G-foliations to tangent bundles of higher order, Nagoya Math. J. 56 (1974), 29-44.
- Crasmareanu, M., Hretcanu, C.E., Golden diğerential geometry, Chaos, Solitons and Fractals (2008), 1229-1238.
- Gezer, A., Cengiz, N., Salimov, A., On integrability of golden Riemannian structures, Turk J. Math. 37 (2013), 693-703.
- Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. (7) (1967), 715-737.
- Houh, C.S., Ishihara, S., Tensor …elds and connections on a cross-section in the tangent bundle of order r, Kodai Math. Sem. Rep. 24 (1972), 234-250.
- Hretcanu, C.E., Submanifolds in Riemannian manifold with golden structure, Workshop on Finsler Geometry and its Applications, Hungary, 2007.
- Hretcanu, C.E., Crasmareanu, M., On some invariant submanifolds in a Riemannian manifold with golden structure, An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 53(1) (2007), 199-211.
- Hretcanu, C.E., Crasmareanu, M., Applications of the golden ratio on Riemannian manifolds, Turk J. Math. 33 (2009), 179-191.
- Morimoto, A., Prolongation of G-structures to tangent bundles of higher order, Nagoya Math. J. 38 (1970), 153-179.
- Morimoto, A., Liftings of tensor …elds and connections to tangent bundles of higher order, Nagoya Math. J. 40 (1970), 99-120.
- Omran, T., Sharğuddin, A., Husain, S.I., Lifts of structures on manifolds, Publications De L’institut Math. 36, 50 (1984), 93-97.
- Özdemir, F., Crasmareanu, M., Geometrical ob jects associated to a substructure, Turk J. Math. 34 (2010), 1-12.
- Özkan, M., Prolongations of golden structures to tangent bundles, Diğer. Geom. Dyn. Syst. (2014), 227-238.
- Pripoae, G.T., Classi…cation of semi-Riemannian almost product structure, BSG Proc. 11, Geometry Balkan Press, Bucharest (2004), 243-251.
- ¸Sahin, B., Akyol, M.A., Golden maps between Golden Riemannian manifolds and constancy of certain maps, Math. Commun. 19 (2014), 1-10.
- Yardımcı, E.H., Yaylı, Y., Golden quaternionic structures, Int. Electron. J. Pure Appl. Math. (2014), 109-125.
- Yano, K., Ishihara, S., Tangent and cotangent bundle, 1973, New York: Marcel Dekker Inc.
- Current address, M. Özkan: Gazi University, Faculty of Science, Department of Mathematics, , Teknikokullar / Ankara - Turkey E-mail address, M. Özkan: ozkanm@gazi.edu.tr Current address, F. Yılmaz: Gazi University, Faculty of Science, Department of Mathematics, , Teknikokullar / Ankara - Turkey E-mail address, F. Yılmaz: fatmayilmaz@gazi.edu.tr