Abstract
Let \(M\) be a smooth manifold, in [3] the authors introduced the notion of generalized metallic structures on \(M\) and studied their integrability with respect to a suitable connection. In this paper, we present the tangent lift of higher order \(r\geq 1\) of these generalized structures and investigate their integrability.
REFERENCES
M. A. Akyol, ‘‘Remark on metallic maps between Metallic Riemannian manifolds and constancy of certain maps,’’ Honam Math. J. 41, 343–356 (2019).
S. Azami, ‘‘General natural metallic structure on tangent bundle,’’ Iran. J. Sci. Technol. Trans. Sci. 42, 81–88 (2018).
A. M. Blaga and A. Nannicini, ‘‘Generalized metallic structures,’’ Rev. Union Math. Argent. 61, 73–86 (2020).
F. Cantrijn, M. Crampin, W. Sarlet, and D. Saunders, ‘‘The canonical isomorphism between \(T^{k}T^{\ast}\) and \(T^{\ast}T^{k}\),’’ C. R. Acad. Sci. (Paris) II 309, 1509–1514 (1989).
G. Cavalcanti, ‘‘New aspects of the \(dd^{c}\)-lemma,’’ Ph.D. Thesis (Univ. of Oxford, 2004).
S. I. Goldberg and K. Yano, ‘‘Polynomial structures on manifolds,’’ Kodai Math. Sem. Rep. 22, 199–218 (1970).
M. Gualtieri, ‘‘Generalized complex geometry,’’ Ph.D. Thesis (Oxford Univ., 2003); arXiv:math/0401221.
N. Hitchin, ‘‘Generalized Calabi–Yau manifold,’’ Quart. J. Math. Oxford 54, 281–308 (2003); arXiv:math/0209099.
C. E. Hreţcanu and M. Crâşmareanu, ‘‘Metallic structures on riemannian manifolds,’’ Rev. Un. Mat. Argentina 54(2), 15–27 (2013).
I. Kólăr, J. Slovák, and P. W. Michor, Natural Operations in Differential Geometry (Springer, Berlin, 1993).
P. M. Kouotchop Wamba and G. F. Wankap Nono, ‘‘Vertical lifts of higher order of multivector fields and applications to poisson geometry,’’ Lobachevskii J. Math. 44, 2967–2981 (2017).
A. Mba, P. M. K. Wamba, and R. P. Nimpa, ‘‘Vertical and horizontal lifts of multivector fiels and applications,’’ Lobachevskii J. Math. 38, 1–15 (2017).
A. Morimoto, ‘‘Lifting of some type of tensors fields and connections to tangent bundles of \(p^{r}\)-velocities,’’ Nagoya Math. 40, 13–31 (1970).
M. Ozkan and F. Yilmaz, ‘‘Metallic structures on differentiable manifolds,’’ J. Sci. Arts 44, 645–660 (2018).
A. Nannicini, ‘‘Calibrated complex structures on the generalized tangent bundle of a Riemannian manifold,’’ J. Geom. Phys. 56, 903–916 (2006).
G. F. Wankap Nono, A. Ntyam, and E. Hinamari Mang-Massou, ‘‘Prolongations of Golden structures to bundles of infinitely near points,’’ J. Indones. Math. Soc. 28, 84–95 (2022).
G. F. Wankap Nono, D. Dehainsala, A. Ntyam, and A. M. Mavamou, ‘‘On lifts of metallic structures related to Weil functors,’’ Differ. Geom.-Dyn. Syst. 24, 215–231 (2022).
K. Yano and M. Kon, Structures on Manifolds, Vol. 3 of Series in Pure Mathematics (World Scientific, Singapore, 1984).
ACKNOWLEDGMENTS
The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their valuable suggestions and remarks which improved the quality of this manuscript.
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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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Wankap Nono, G.F., Kouotchop Wamba, P.M. & Toukap Wankap, E.C. Tangent Generalized Metallic Structures of Higher Order. Lobachevskii J Math 44, 5493–5501 (2023). https://doi.org/10.1134/S1995080223120260
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DOI: https://doi.org/10.1134/S1995080223120260