Araştırma Makalesi
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A New Structure on Manifolds: Silver Structure

Yıl 2016, Cilt: 9 Sayı: 2, 59 - 69, 30.10.2016
https://doi.org/10.36890/iejg.584592

Öz

Kaynakça

  • [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.
Yıl 2016, Cilt: 9 Sayı: 2, 59 - 69, 30.10.2016
https://doi.org/10.36890/iejg.584592

Öz

Kaynakça

  • [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.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Mustafa Özkan

Betül Peltek Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 9 Sayı: 2

Kaynak Göster

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. Ekim 2016;9(2):59-69. doi:10.36890/iejg.584592
Chicago Özkan, Mustafa, ve Betül Peltek. “A New Structure on Manifolds: Silver Structure”. International Electronic Journal of Geometry 9, sy. 2 (Ekim 2016): 59-69. https://doi.org/10.36890/iejg.584592.
EndNote Özkan M, Peltek B (01 Ekim 2016) A New Structure on Manifolds: Silver Structure. International Electronic Journal of Geometry 9 2 59–69.
IEEE M. Özkan ve B. Peltek, “A New Structure on Manifolds: Silver Structure”, Int. Electron. J. Geom., c. 9, sy. 2, ss. 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 (Ekim 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 ve Betül Peltek. “A New Structure on Manifolds: Silver Structure”. International Electronic Journal of Geometry, c. 9, sy. 2, 2016, ss. 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.