A Survey on Metallic Vector Fields

Document Type : Original Scientific Paper

Authors

‎Department of Pure Mathematics‎, ‎Faculty of Science‎, ‎‎Imam Khomeini International University, ‎Qazvin‎, ‎I‎. ‎R‎. ‎Iran

10.22052/mir.2025.257341.1532

Abstract

‎This document introduces the idea of metallic vector fields in the framework of semi-Riemannian manifolds‎. ‎Then‎, ‎we study the geometry of such vector fields on closed and compact manifolds‎. ‎The existence of metallic fields on immersed submanifolds will also be investigated‎. ‎Finally‎, ‎we investigate metallic vector fields on warped product manifolds‎.

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[1] S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Cambridge University Press, 2019.
[2] S. Deshmukh, Geometry of conformal vector fields, Arab. J. Math. Sci. 23 (2017) 44-73, https://doi.org/10.1016/j.ajmsc.2016.09.003.
[3] K. Yano, The Theory of Lie Derivatives and its Applications, Dover Publications, Inc., Mineola, NY, 2020.
[4] G. Fasihi-Ramandi, S. Azami and M. A. Choudhary, On hyperbolic Ricci solitons, Chaos Soliton Fract. 193 (2025) #116095, https://doi.org/10.1016/j.chaos.2025.116095.
[5] F. Shahmkhali, G. Fasihi-Ramandi and U. C. De, Some characterizations for compact hyperbolic Ricci solitons admitting 2-Conformal vector fields, Filomat 39 (2025) 7953 -7961.
[6] A. García-Parrado and J. M. M. Senovilla, Bi-conformal vector fields and their applications, Class. Quantum Grav. 21 (2004) #2153, https://doi.org/10.1088/0264-9381/21/8/017.
[7] S. Azami and U. C. De, Ricci bi-conformal vector fields on Lorentzian four dimensional generalized symmetric spaces, Filomat 38 (2024) 3157-3164, https://doi.org/10.2298/FIL2409157A.
[8] S. Azami and U. C. De, Ricci bi-conformal vector fields on Lorentzian fivedimensional two-step nilpotent Lie groups, Hacet. J. Math. Stat. 53 (2024) 1118 - 1129.
[9] S. Azami and G. Fasihi-Ramandi, Ricci bi-conformal vector fields on Siklos spacetimes, Math. Interdisc. Res. 9 (2024) 45 -76, https://doi.org/10.22052/mir.2023.252926.1408.
[10] S. Azami and M. Jafari, Ricci bi-conformal vector fields on homogeneous Godel-type spacetimes, J. Nonlinear Math. Phys. 30 (2023) 1700 - 1718, https://doi.org/10.1007/s44198-023-00151-3.
[11] M. Sohrabpour and S. Azami, Ricci bi-conformal vector fields on Lorentzian Walker manifolds of low dimension, Lobachevskii J. Math. 44 (2023) 5437-5443, https://doi.org/10.1134/S1995080223120338.
[12] A. M. Blaga, On warped product gradient \eta-Ricci solitons, Filomat 31 (2017) 5791 - 5801, https://doi.org/10.2298/FIL1718791B.
[13] A. M. Blaga and C. Özgür, Killing and 2-Killing vector fields on doubly warped products, Mathematics 11 (2023) #4983, https://doi.org/10.3390/math11244983.
[14] R. Deszcz, On pseudo symmetric spaces, Bull. Soc. Math. Belg., Ser. A 44 (1992) 1 - 34.
[15] I. Hinterleitner and V. A. Kiosak, \phi(Ric)-vector fields in Riemannian spaces, Arch. Math. 44 (2008) 385 - 390.
[16] A. M. Blaga and C. Özgür, Results of hyperbolic Ricci solitons, Symmetry 15 (2023) #1548, https://doi.org/10.3390/sym15081548.
[17] C. Özgür and N. Y. Özgür, Classification of metallic shaped hypersurfaces in real space forms, Turkish J. Math. 39 (2015) 784 - 794, https://doi.org/10.3906/mat-1408-17.
[18] Y. Zhao and X. Liu, A class of special hypersurfaces in real space forms, J. Funct. Spaces 2016 (2016) #8796938,
https://doi.org/10.1155/2016/8796938.
[19] R. Deszcz, L. Verstraelen and S. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica 22 (1994) 167 - 179.