Research Article
Year 2025,
Volume: 18 Issue: 1, 14 - 32, 24.04.2025
Abstract
References
- Akyol M.A.: Remark on metallic maps between Metallic Riemannian manifolds and constancy of certain maps, Honam Math. J. 41(2019), No. 2, 343-356.
- Blaga A.M., Nannicini A.: Generalized metallic structures, Revista de la Unión Mathematica Argentina, 61(2020), No1, 73-86.
- Cabras A., Kolar I., Prolongation of tangent valued forms to Weil bundles, Archivum Mathematicum, Vol. 21 (1995), No. 2, 139-145.
- Crasmareanu M., Hretcanu C.E.: Golden differential geometry, Chaos Solitons Fractals 38 (2008), no. 5, 1229-1238.
- Debecki J., Krakow, Linear natural operators lifting p-vectors to tensors of type (q, 0) on Weil bundles, Czechoslovak Mathematical Journal, vol. 66(141), (2016), P. 511-525.
- Doupovec M., Kures M.: Some geometric constructions on Frobenius Weil bundles, Differential geometry and its applications, vol. 35, (2014), P. 143-149.
- Gancarzewicz J., Mikulski M., Pagoda Z.: Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J., 135(1994), 1-14.
- Goldberg S.I., Yano K.: Polynomial structures on manifolds, Kodai Math. Sem. Rep. 22 (1970), 199-218.
- Gualtieri M.: Generalized complex Geometry, PhD. Thesis, Oxford University, 2003 (math.DG/0401221).
- Gualtieri M.: Generalized complex geometry, Annals of Mathematics, 174(2011), 75-123.
- Lee J.M.:Introduction to Riemannian Manifolds, Springer Cham, 2018.
- Hitchin N.: Generalized Calabi-Yau manifold, Quart. J. Math. Oxford, 54(2003), 281-308(math.DG/0209099).
- Hretcanu C.E., Crâ¸smareanu M.: Metallic structures on riemannian manifolds, Rev. Un. Mat. Argentina 54(2013), No. 2, 15-27
- Kolar I.: On the geometry of Weil bundles, Differential geometry and its applications, Vol. 35, (2014), 136-142.
- Kolar I.: Covariant approach to natural transformations of Weil functors, Commentationes Mathematicae Universitatis Carolinea, Vol. 27, (1986), No. 4, 723-729.
- Kolar I., Michor P., Slovak J.: Natural operations in differential geometry, Springer-Verlag. 1993.
- Kouotchop Wamba P.M. & Ntyam A.: Prolongations of Dirac structures related to Weil bundles, Lobachevskii Journal of Mathamtics, 35(2014), 106-121.
- Kouotchop Wamba P.M., Mba A.: Characterization of some natural transformations between the bundle functors $T^{A}\circ T^{\ast}$ and $T^{\ast}\circ T^{A}$ on $\mathcal{M}f_{m}$, Imhotep Mathematical Journal, vol. 3, (2018).
- Ntyam A., Wouafo Kamga J.: New versions of curvature and torsion formulas for the complete lifting of a linear connection to Weil bundles , Annales Polonici Mathmatici, 82(2003), 233-240.
- Nannicini A.: Calibrated complex structures on the generalized tangent bundle of a Riemannian manifold, Journal of Geometry and Physics, 56(2006), 903-916.
- Ozkan M.: Prolongations of golden structures to tangent bundles of order r, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 65(2016), N◦1, 35-47.
- Ozkan M., Yilmaz F.: Metallic structures on differentiable manifolds, Journal of Science and Arts, 44(2018), 645-660.
- De Spinadel V.W.: The metallic means and design, Nexus II: Architecture and Mathematics (Mantua, 1998), 143-157, Collana Gli Studi, 5, Erba, Fucecchio, 1998.
- Slovák J.:Prolongations of connections and spray with respect to Weil functors, Rend Circ. Mat. Palermo Suppl., 14(1987), 143-155.
- Wankap Nono G.F., Kouotchop Wamba P.M., Toukap Wankap E.C.: Tangent generalized metallic structures of higher order, Lobachevskii Journal of Mathamtics, 44(2023), 5097-5115.
- Zeina A.A.: The Golden ratio and its impact on architural design, international Design journal, 12(2021), 77-90.
Year 2025,
Volume: 18 Issue: 1, 14 - 32, 24.04.2025
Abstract
Let (A, l) be a Weil-Frobenius algebra, M a smooth manifold. In this paper, we study the prolongations of generalized metallic structures on manifold M to its Weil bundle TAM and we investigate some of their properties. In particular, we study the prolongation of calibrated generalized product structures and calibrated complex structures induced by metallic structures on M.
Keywords
Weil-Frobenius algebra Weil functor $A$-jet generalized metallic structures natural transformations
References
- Akyol M.A.: Remark on metallic maps between Metallic Riemannian manifolds and constancy of certain maps, Honam Math. J. 41(2019), No. 2, 343-356.
- Blaga A.M., Nannicini A.: Generalized metallic structures, Revista de la Unión Mathematica Argentina, 61(2020), No1, 73-86.
- Cabras A., Kolar I., Prolongation of tangent valued forms to Weil bundles, Archivum Mathematicum, Vol. 21 (1995), No. 2, 139-145.
- Crasmareanu M., Hretcanu C.E.: Golden differential geometry, Chaos Solitons Fractals 38 (2008), no. 5, 1229-1238.
- Debecki J., Krakow, Linear natural operators lifting p-vectors to tensors of type (q, 0) on Weil bundles, Czechoslovak Mathematical Journal, vol. 66(141), (2016), P. 511-525.
- Doupovec M., Kures M.: Some geometric constructions on Frobenius Weil bundles, Differential geometry and its applications, vol. 35, (2014), P. 143-149.
- Gancarzewicz J., Mikulski M., Pagoda Z.: Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J., 135(1994), 1-14.
- Goldberg S.I., Yano K.: Polynomial structures on manifolds, Kodai Math. Sem. Rep. 22 (1970), 199-218.
- Gualtieri M.: Generalized complex Geometry, PhD. Thesis, Oxford University, 2003 (math.DG/0401221).
- Gualtieri M.: Generalized complex geometry, Annals of Mathematics, 174(2011), 75-123.
- Lee J.M.:Introduction to Riemannian Manifolds, Springer Cham, 2018.
- Hitchin N.: Generalized Calabi-Yau manifold, Quart. J. Math. Oxford, 54(2003), 281-308(math.DG/0209099).
- Hretcanu C.E., Crâ¸smareanu M.: Metallic structures on riemannian manifolds, Rev. Un. Mat. Argentina 54(2013), No. 2, 15-27
- Kolar I.: On the geometry of Weil bundles, Differential geometry and its applications, Vol. 35, (2014), 136-142.
- Kolar I.: Covariant approach to natural transformations of Weil functors, Commentationes Mathematicae Universitatis Carolinea, Vol. 27, (1986), No. 4, 723-729.
- Kolar I., Michor P., Slovak J.: Natural operations in differential geometry, Springer-Verlag. 1993.
- Kouotchop Wamba P.M. & Ntyam A.: Prolongations of Dirac structures related to Weil bundles, Lobachevskii Journal of Mathamtics, 35(2014), 106-121.
- Kouotchop Wamba P.M., Mba A.: Characterization of some natural transformations between the bundle functors $T^{A}\circ T^{\ast}$ and $T^{\ast}\circ T^{A}$ on $\mathcal{M}f_{m}$, Imhotep Mathematical Journal, vol. 3, (2018).
- Ntyam A., Wouafo Kamga J.: New versions of curvature and torsion formulas for the complete lifting of a linear connection to Weil bundles , Annales Polonici Mathmatici, 82(2003), 233-240.
- Nannicini A.: Calibrated complex structures on the generalized tangent bundle of a Riemannian manifold, Journal of Geometry and Physics, 56(2006), 903-916.
- Ozkan M.: Prolongations of golden structures to tangent bundles of order r, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 65(2016), N◦1, 35-47.
- Ozkan M., Yilmaz F.: Metallic structures on differentiable manifolds, Journal of Science and Arts, 44(2018), 645-660.
- De Spinadel V.W.: The metallic means and design, Nexus II: Architecture and Mathematics (Mantua, 1998), 143-157, Collana Gli Studi, 5, Erba, Fucecchio, 1998.
- Slovák J.:Prolongations of connections and spray with respect to Weil functors, Rend Circ. Mat. Palermo Suppl., 14(1987), 143-155.
- Wankap Nono G.F., Kouotchop Wamba P.M., Toukap Wankap E.C.: Tangent generalized metallic structures of higher order, Lobachevskii Journal of Mathamtics, 44(2023), 5097-5115.
- Zeina A.A.: The Golden ratio and its impact on architural design, international Design journal, 12(2021), 77-90.
There are 26 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | April 20, 2025 |
| Publication Date | April 24, 2025 |
| Submission Date | October 4, 2024 |
| Acceptance Date | February 25, 2025 |
| Published in Issue | Year 2025 Volume: 18 Issue: 1 |
