[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.
[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.
[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.
[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.
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.