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Nickel Structure on a Differentiable Manifold

Ibrahim Isah, Mustapha Usman Baba, Nafisatu Muhammad Usman, Ahmad Nasidi, Umar, Aminu Muhammad Yusuf, Tijjani Lawal Hassan

Abstract

We introduce a novel geometric structure on a differentiable manifold, which we call a nickel structure. This structure is defined by a tensor field ? of type (1,1) satisfying the algebraic equation ?2 ???3?= 0, where ? denotes the identity tensor. The defining equation leads to a natural decomposition of the tangent bundle into invariant subspaces characterized by two distinct eigenvalues, we determine the integrability of this decomposition through related almost product structure. We also, investigate the connection and parallelism of the nickel structure, and whether ? is preserved under a specific affine connection, including the Schouten and Vr? ?nceanu connection. Furthermore, we extend the concept of Riemannian geometry by defining a nickel Riemannian structure, where ? is compatible with the Riemannian metric ?.

Keywords

almost product structureNickel structureintegrabilityNickel Riemannian Manifold

References

[1] V.W. de Spinadel, “The Metallic Means and Design,” in Nexus II: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba, 1998, pp. 141– [Online]. Available: http://www.nexusjournal.com/conferences/N1998-Spinadel.html [2] R. Herz-fischler, “two-columns.tex ],” 2000. [3] A. M. Blaga and A. Nannicini, “Generalized metallic structures,” pp. 1–19, 2018, [Online]. Available: http://arxiv.org/abs/1807.08308 [4] M. Crasmareanu and C. E. Hre?canu, “Golden differential geometry,” Chaos, Solitons and Fractals, vol. 38, no. 5, pp. 1229–1238, 2008, doi: 10.1016/j.chaos.2008.04.007. [5] M. Özkan and B. Peltek, “A New Structure on Manifolds: Silver Structure,” Int. Electron. J. Geom., vol. 9, no. 2PAGE, pp. 59–69, 2016. [6] I. Isah and M. A. Isah, “On integrability of silver riemannian structure,” Int. J. Adv. Acad. Res. | ISSN 2488-9849, vol. 7, no. December, pp. 57–65, 2021. [7] P. K. Pandey, “Bronze differential geometry,” vol. 4, no. 4, pp. 973–980, 2018. [8] M. Yano, K., Kon, Structures on Manifolds. [9] A. Gezer and Ç. KARAMAN, “On metallic Riemannian structures,” Turkish J. Math., vol. 39, no. 6, pp. 954–962, 2015. [10] M. Özkan and F. Yilmaz, “Metallic Structures on Differentiable Manifolds,” pp. 1–14, 2018, [Online]. Available: http://arxiv.org/abs/1807.04360 [11] C.-E. Hretcanu and M. Crasmareanu, “Metallic structures on Riemannian manifolds,” Rev. Un. Mat. Argentina, vol. 54, no. 2, pp. 15–27, 2013. [12] C. Procesi, “Lie groups: an approach through invariants and representations,” Springer, vol. 115, 2007. [13] A. Singh, R. K. Pandey, and S. Khare, “Parallelism of distributions and geodesics on F(2K + S; S)-structure Lagrangian manifolds,” Int. J. Contemp. Math. Sci., vol. 9, pp. 515–522, 2014, doi: 10.12988/ijcms.2014.4668. [14] F. Özdemir and M. Cr??m?reanu, “Geometrical objects associated to a substructure,” Turkish J. Math., vol. 35, no. 4, pp. 717–728, 2011, doi: 10.3906/mat-0710-33.

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