In this work, we study a hypersurface immersed in specific types of cylindrically symmetric static space-times, then we identify the gauge fields of the Lagrangian that minimizes the area beside the Noether symmetries. We show that these symmetries are part of the Killing algebra of cylindrically symmetric static space-times. By using Noether’s theorem, we construct the conserved vector fields for the minimal hypersurface.
[1] F. Ali, T. Feroze, and S. Ali, Complete classification of spherically symmetric static space-times via Noether symmetries, Theore. Math. Phys., 184 (2015), 973–985.
[2] F. Ali and T. Feroze, Complete classification of cylindrically symmetric static spacetimes and the corresponding conservation laws, Mathematics, 4(3) (2016), 50.
[3] A. Aslam and A. Qadir, Noether symmetries of the area-minimizing lagrangian, J. Appl. Math., 2012 (2012), Article ID 532690.
[4] R. Bakhshandeh-Chamazkoti, Symmetry analysis of the charged squashed Kaluza–Klein black hole metric, Math. Methods Appl. Sci., 39(12) (2016), 3163–3172.
[5] N. Bıla, Lie groups applications to minimal surfaces PDE, Differ. Geom. Dyn. Syst., 1(1) (1999), 1–9.
[6] G. W. Bluman, A. F. Cheviakov, and S. Anco, Applications of symmetry methods to partial differential equations, Springer, 2010.
[7] M. S. Hashemi and D. Baleanu, Lie symmetry analysis of fractional differential equations, CRC Press, 2020.
[8] V. Lahno, R. Zhdanov, and O. Magda, Group classification and exact solutions of nonlinear wave equations, Acta Appl. Math., 91 (2006), 253–313.
[9] A. Mohammadpouri, M. S. Hashemi, and S. Samaei, Noether symmetries and isometries of the area-minimizing Lagrangian on vacuum classes of pp-waves, Eur. Phys. J. Plus., 138(112) (2023).
[10] P. J. Olver, Applications of Lie groups to differential equations, Springer Science & Business Media, 1993.
[11] A. Peterson and S. Taylor, Locally isometric families of minimal surfaces, Balkan J. Geom. Appl., 13(2) (2008), 80–85.
[12] A. Qadir, M. Sharif, and M. Ziad, Homotheties of cylindrically symmetric static manifolds and their global extension, Classical Quantum Gravit, 17(2) (2000), 345–349.
[13] V. Shirvani and M. Nadjafikhah, Symmetry analysis and conservation laws for higher order CamassaHolm equation, Comput. Methods Differ. Equ., 8(2) (2020), 135–145.
[14] M. Tsamparlis, A. Paliathanasis, and A. Qadir, Noether symmetries and isometries of the minimal surface Lagrangian under constant volume in a Riemannian space, Int. J. Geom. Methods Mod. Phys., 12(1) (2015), Article ID 1550003-290.
Mohammadpouri, A. , Hashemi, M. S. , Samaei, S. and Salar Anvar, S. (2024). Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times. Computational Methods for Differential Equations, 13(1), 249-257. doi: 10.22034/cmde.2024.60285.2572
MLA
Mohammadpouri, A. , , Hashemi, M. S. , , Samaei, S. , and Salar Anvar, S. . "Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times", Computational Methods for Differential Equations, 13, 1, 2024, 249-257. doi: 10.22034/cmde.2024.60285.2572
HARVARD
Mohammadpouri, A., Hashemi, M. S., Samaei, S., Salar Anvar, S. (2024). 'Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times', Computational Methods for Differential Equations, 13(1), pp. 249-257. doi: 10.22034/cmde.2024.60285.2572
CHICAGO
A. Mohammadpouri , M. S. Hashemi , S. Samaei and S. Salar Anvar, "Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times," Computational Methods for Differential Equations, 13 1 (2024): 249-257, doi: 10.22034/cmde.2024.60285.2572
VANCOUVER
Mohammadpouri, A., Hashemi, M. S., Samaei, S., Salar Anvar, S. Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times. Computational Methods for Differential Equations, 2024; 13(1): 249-257. doi: 10.22034/cmde.2024.60285.2572
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