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PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r

Year 2016, Volume: 65 Issue: 1, 35 - 48, 01.02.2016
https://doi.org/10.1501/Commua1_0000000742

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

  • 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
Year 2016, Volume: 65 Issue: 1, 35 - 48, 01.02.2016
https://doi.org/10.1501/Commua1_0000000742

Abstract

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
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Mustafa Özkan This is me

Fatma Yılmaz This is me

Publication Date February 1, 2016
Published in Issue Year 2016 Volume: 65 Issue: 1

Cite

APA Özkan, M., & Yılmaz, F. (2016). PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(1), 35-48. https://doi.org/10.1501/Commua1_0000000742
AMA Özkan M, Yılmaz F. PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2016;65(1):35-48. doi:10.1501/Commua1_0000000742
Chicago Özkan, Mustafa, and Fatma Yılmaz. “PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER R”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 1 (February 2016): 35-48. https://doi.org/10.1501/Commua1_0000000742.
EndNote Özkan M, Yılmaz F (February 1, 2016) PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 1 35–48.
IEEE M. Özkan and F. Yılmaz, “PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 1, pp. 35–48, 2016, doi: 10.1501/Commua1_0000000742.
ISNAD Özkan, Mustafa - Yılmaz, Fatma. “PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER R”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/1 (February 2016), 35-48. https://doi.org/10.1501/Commua1_0000000742.
JAMA Özkan M, Yılmaz F. PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:35–48.
MLA Özkan, Mustafa and Fatma Yılmaz. “PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER R”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 1, 2016, pp. 35-48, doi:10.1501/Commua1_0000000742.
Vancouver Özkan M, Yılmaz F. PROLONGATIONS OF GOLDEN STRUCTURES TO TANGENT BUNDLES OF ORDER r. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(1):35-48.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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