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A New Structure on Manifolds: Silver Structure

Year 2016, Volume: 9 Issue: 2, 59 - 69, 30.10.2016
https://doi.org/10.36890/iejg.584592

Abstract

References

  • [1] Bejancu, A. and Farran, H.R., Foliations and Geometric Structures. Mathematics and its Applications, vol. 580, Springer, 2006.
  • [2] Chandra, M. and Rani, M., Categorization of fractal plants. Chaos, Solitons & Fractals 41 (2009), no.3, 1442–1447.
  • [3] Crasmareanu, M. and Hre¸tcanu, C.E., Golden differential geometry. Chaos, Solitons & Fractals 38 (2008), no.5, 1229–1238.
  • [4] Cruceanu, V., On almost biproduct complex manifolds. An. Ştiin¸t. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) 52 (2006), no.1, 5–24.
  • [5] Das, L.S., Nikic, J. and Nivas, R., Parallelism of distributions and geodesics on F (a1, a2, ..., an) −structure Lagrangian manifolds. Diff.Geom. Dyn. Syst. 8 (2006), 82–89.
  • [6] Gezer, A., Cengiz, N. and Salimov, A., On integrability of Golden Riemannian structures. Turk. J. Math. 37 (2013), no.4, 693–703.
  • [7] Gezer, A. and Karaman C., Golden-Hessian structures. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86 (2016), no:1, 41–46.
  • [8] Gray, A., Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 (1967), 715–737.
  • [9] Hinterleitner, I., Mikeš, J. and Peška, P., On F ε-planar mappings of (pseudo-) Riemannian manifolds. Arch. Math. (Brno) 50 (2014), no.5,287–295.
  • [10] Hrdina, J., Geometry of almost Cliffordian manifolds: Nijenhuis tensor. Miskolc Math. Notes 14 (2013), no.2, 583–589.
  • [11] Hrdina, J. and Vašik, P., Geometry of almost Cliffordian manifolds: classes of subordinated connections. Turk. J. Math. 38 (2014), no.1, 179–190.
  • [12] Horadam, A.F., Pell identities. Fibonacci Quart. 9 (1971), no.3, 245–252, 263.
  • [13] Hretcanu, C.E., Submanifolds in Riemannian manifold with Golden structure. Workshop on Finsler geometry and its applications, Hungary, 2007.
  • [14] Hre¸tcanu, C.E. and Crasmareanu, M., On some invariant submanifolds in a Riemannian manifold with Golden structure. An. Ştiin¸t. Univ.Al. I. Cuza Ias¸i. Mat. (N.S.) 53 (2007), suppl. 1, 199–211.
  • [15] Hre¸tcanu, C.E. and Crasmareanu, M., Applications of the Golden ratio on Riemannian manifolds. Turk J. Math. 33 (2009), no.2, 179–191.
  • [16] Kocer, E.G., Tuglu, N. and Stakhov, A., Hyperbolic functions with second order recurrence sequences. ARS Combinatoria 88 (2008), 65–81.
  • [17] Mikeš, J., et al., Differential Geometry of Special Mappings. Palacký University, Faculty of Science, Olomouc, 2015.
  • [18] Mikeš, J., Jukl, M. and Juklovă, L., Some results on traceless decompositon of tensors. J. Math. Sci. 174 (2011), no.5, 627–640.
  • [19] Mikeš, J. and Sinyukov, N.S., On quasiplanar mappings of spaces of affine connection. Sov. Math. 27 (1983), 63–70.
  • [20] Primo, A. and Reyes, E., Some algebraic and geometric properties of the silver number. Mathematics and Informatics Quarterly 18 (2007), no. 1 .
  • [21] Procesi, C., Lie Groups: An Approach Through Invariants and Representations. Universitext, Springer, 2007.
  • [22] Özdemir, F. and Crasmareanu, M., Geometrical objects associated to a substructure. Turk J. Math. 35 (2011), no.4, 717–728.
  • [23] Özkan, M. and Peltek, B., Silver differential geometry. II. International Eurasian Conference on Mathematical Sciences and Applications,Sarajevo-Bosnia and Herzegovina, 2013, 273.
  • [24] Özkan, M., Prolongations of Golden structures to tangent bundles. Differ. Geom. Dyn. Syst. 16 (2014), 227–238.
  • [25] Özkan, M., Çıtlak, A.A. and Taylan, E., Prolongations of Golden structure to tangent bundle of order 2. GU J. Sci. 28 (2015), no.2, 253–258.
  • [26] Özkan, M. and Yılmaz, F., Prolongations of Golden structures to tangent bundles of order r. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 65 (2016), no.1, 35–47.
  • [27] Pripoae, G.T., Classification of semi-Riemannian almost product structure. Proceedings of The Conference of Applied Differential Geometry - General Relativity and the Workshop on Global Analysis, Differential Geometry and Lie Algebras, 2002, 243–251.
  • [28] Savas, M., Ozkan, M. and Iscan, M., On 4−dimensional Golden-Walker structures, Journal of Science and Arts, (2016), no.2(35), 89–100.
  • [29] Şahin, B. and Akyol, M.A., Golden maps between Golden Riemannian manifolds and constancy of certain maps. Math. Commun. 19 (2014), no.2, 333–342.
  • [30] Yano, K. and Ishihara, S., Tangent and Cotangent Bundle. Marcel Dekker Inc., New York, 1973.
  • [31] Yano, K. and Kon, M., Structures on Manifolds, Series in Pure Mathematics. Vol. 3, World Scientific, Singapore, 1984. aylı, Y., Golden quaternionic structures. Int. Electron. J. Pure Appl. Math. 7 (2014), no.3, 109–125.
Year 2016, Volume: 9 Issue: 2, 59 - 69, 30.10.2016
https://doi.org/10.36890/iejg.584592

Abstract

References

  • [1] Bejancu, A. and Farran, H.R., Foliations and Geometric Structures. Mathematics and its Applications, vol. 580, Springer, 2006.
  • [2] Chandra, M. and Rani, M., Categorization of fractal plants. Chaos, Solitons & Fractals 41 (2009), no.3, 1442–1447.
  • [3] Crasmareanu, M. and Hre¸tcanu, C.E., Golden differential geometry. Chaos, Solitons & Fractals 38 (2008), no.5, 1229–1238.
  • [4] Cruceanu, V., On almost biproduct complex manifolds. An. Ştiin¸t. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) 52 (2006), no.1, 5–24.
  • [5] Das, L.S., Nikic, J. and Nivas, R., Parallelism of distributions and geodesics on F (a1, a2, ..., an) −structure Lagrangian manifolds. Diff.Geom. Dyn. Syst. 8 (2006), 82–89.
  • [6] Gezer, A., Cengiz, N. and Salimov, A., On integrability of Golden Riemannian structures. Turk. J. Math. 37 (2013), no.4, 693–703.
  • [7] Gezer, A. and Karaman C., Golden-Hessian structures. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86 (2016), no:1, 41–46.
  • [8] Gray, A., Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 (1967), 715–737.
  • [9] Hinterleitner, I., Mikeš, J. and Peška, P., On F ε-planar mappings of (pseudo-) Riemannian manifolds. Arch. Math. (Brno) 50 (2014), no.5,287–295.
  • [10] Hrdina, J., Geometry of almost Cliffordian manifolds: Nijenhuis tensor. Miskolc Math. Notes 14 (2013), no.2, 583–589.
  • [11] Hrdina, J. and Vašik, P., Geometry of almost Cliffordian manifolds: classes of subordinated connections. Turk. J. Math. 38 (2014), no.1, 179–190.
  • [12] Horadam, A.F., Pell identities. Fibonacci Quart. 9 (1971), no.3, 245–252, 263.
  • [13] Hretcanu, C.E., Submanifolds in Riemannian manifold with Golden structure. Workshop on Finsler geometry and its applications, Hungary, 2007.
  • [14] Hre¸tcanu, C.E. and Crasmareanu, M., On some invariant submanifolds in a Riemannian manifold with Golden structure. An. Ştiin¸t. Univ.Al. I. Cuza Ias¸i. Mat. (N.S.) 53 (2007), suppl. 1, 199–211.
  • [15] Hre¸tcanu, C.E. and Crasmareanu, M., Applications of the Golden ratio on Riemannian manifolds. Turk J. Math. 33 (2009), no.2, 179–191.
  • [16] Kocer, E.G., Tuglu, N. and Stakhov, A., Hyperbolic functions with second order recurrence sequences. ARS Combinatoria 88 (2008), 65–81.
  • [17] Mikeš, J., et al., Differential Geometry of Special Mappings. Palacký University, Faculty of Science, Olomouc, 2015.
  • [18] Mikeš, J., Jukl, M. and Juklovă, L., Some results on traceless decompositon of tensors. J. Math. Sci. 174 (2011), no.5, 627–640.
  • [19] Mikeš, J. and Sinyukov, N.S., On quasiplanar mappings of spaces of affine connection. Sov. Math. 27 (1983), 63–70.
  • [20] Primo, A. and Reyes, E., Some algebraic and geometric properties of the silver number. Mathematics and Informatics Quarterly 18 (2007), no. 1 .
  • [21] Procesi, C., Lie Groups: An Approach Through Invariants and Representations. Universitext, Springer, 2007.
  • [22] Özdemir, F. and Crasmareanu, M., Geometrical objects associated to a substructure. Turk J. Math. 35 (2011), no.4, 717–728.
  • [23] Özkan, M. and Peltek, B., Silver differential geometry. II. International Eurasian Conference on Mathematical Sciences and Applications,Sarajevo-Bosnia and Herzegovina, 2013, 273.
  • [24] Özkan, M., Prolongations of Golden structures to tangent bundles. Differ. Geom. Dyn. Syst. 16 (2014), 227–238.
  • [25] Özkan, M., Çıtlak, A.A. and Taylan, E., Prolongations of Golden structure to tangent bundle of order 2. GU J. Sci. 28 (2015), no.2, 253–258.
  • [26] Özkan, M. and Yılmaz, F., Prolongations of Golden structures to tangent bundles of order r. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 65 (2016), no.1, 35–47.
  • [27] Pripoae, G.T., Classification of semi-Riemannian almost product structure. Proceedings of The Conference of Applied Differential Geometry - General Relativity and the Workshop on Global Analysis, Differential Geometry and Lie Algebras, 2002, 243–251.
  • [28] Savas, M., Ozkan, M. and Iscan, M., On 4−dimensional Golden-Walker structures, Journal of Science and Arts, (2016), no.2(35), 89–100.
  • [29] Şahin, B. and Akyol, M.A., Golden maps between Golden Riemannian manifolds and constancy of certain maps. Math. Commun. 19 (2014), no.2, 333–342.
  • [30] Yano, K. and Ishihara, S., Tangent and Cotangent Bundle. Marcel Dekker Inc., New York, 1973.
  • [31] Yano, K. and Kon, M., Structures on Manifolds, Series in Pure Mathematics. Vol. 3, World Scientific, Singapore, 1984. aylı, Y., Golden quaternionic structures. Int. Electron. J. Pure Appl. Math. 7 (2014), no.3, 109–125.
There are 31 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mustafa Özkan

Betül Peltek This is me

Publication Date October 30, 2016
Published in Issue Year 2016 Volume: 9 Issue: 2

Cite

APA Özkan, M., & Peltek, B. (2016). A New Structure on Manifolds: Silver Structure. International Electronic Journal of Geometry, 9(2), 59-69. https://doi.org/10.36890/iejg.584592
AMA Özkan M, Peltek B. A New Structure on Manifolds: Silver Structure. Int. Electron. J. Geom. October 2016;9(2):59-69. doi:10.36890/iejg.584592
Chicago Özkan, Mustafa, and Betül Peltek. “A New Structure on Manifolds: Silver Structure”. International Electronic Journal of Geometry 9, no. 2 (October 2016): 59-69. https://doi.org/10.36890/iejg.584592.
EndNote Özkan M, Peltek B (October 1, 2016) A New Structure on Manifolds: Silver Structure. International Electronic Journal of Geometry 9 2 59–69.
IEEE M. Özkan and B. Peltek, “A New Structure on Manifolds: Silver Structure”, Int. Electron. J. Geom., vol. 9, no. 2, pp. 59–69, 2016, doi: 10.36890/iejg.584592.
ISNAD Özkan, Mustafa - Peltek, Betül. “A New Structure on Manifolds: Silver Structure”. International Electronic Journal of Geometry 9/2 (October 2016), 59-69. https://doi.org/10.36890/iejg.584592.
JAMA Özkan M, Peltek B. A New Structure on Manifolds: Silver Structure. Int. Electron. J. Geom. 2016;9:59–69.
MLA Özkan, Mustafa and Betül Peltek. “A New Structure on Manifolds: Silver Structure”. International Electronic Journal of Geometry, vol. 9, no. 2, 2016, pp. 59-69, doi:10.36890/iejg.584592.
Vancouver Özkan M, Peltek B. A New Structure on Manifolds: Silver Structure. Int. Electron. J. Geom. 2016;9(2):59-6.