×
Yücesan, Ahmet; Oral, Mehmet

Elastica on 2-dimensional anti-de Sitter space. (English) Zbl 1211.53027

Int. J. Geom. Methods Mod. Phys. 8, No. 1, 107-113 (2011).
Summary: We derive differential equations for non-null elastic curves on 2-dimensional anti-de Sitter space. Then, we solve these differential equations in terms of Jacobi elliptic functions. Also, we give a relation between curvature and torsion of elastic curve on 2-dimensional anti-de Sitter space.

Cited in 5 Documents

MSC:

53A25 Differential line geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
74B20 Nonlinear elasticity

Keywords:

elastic curve; Euler-Lagrange equations; Darboux frame; geodesic curvature; anti-de Sitter space
Cite Review PDF
Full Text: DOI

References:

[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (US Government Printing Office, Washington DC, 1964) pp. 567–626.
[2] Beem J. K., Global Lorentzian Geometry (1981) · Zbl 0462.53001
[3] M. Barros, Solutions of the Betchov-Da Rios Soliton Equation in the Anti-de Sitter 3-Space, New Approaches in Nonlinear Analysis (Hadronic Press, Florida, 1999) pp. 51–71.
[4] Bolza O., Vorlesungen uber Variationsrechnung (1949)
[5] DOI: 10.1007/BF02519034 · Zbl 0830.65083 · doi:10.1007/BF02519034
[6] DOI: 10.1016/B978-0-12-460510-7.50009-4 · doi:10.1016/B978-0-12-460510-7.50009-4
[7] DOI: 10.1016/0370-2693(90)90491-N · doi:10.1016/0370-2693(90)90491-N
[8] DOI: 10.1103/RevModPhys.74.953 · doi:10.1103/RevModPhys.74.953
[9] Langer J., J. Diff. Geom. 20 pp 1–
[10] O’Neill B., Elementary Differential Geometry Second Edition (1997)
[11] O’Neill B., Semi-Riemann Geometry with Applications to Relativity (1993)
[12] DOI: 10.1063/1.2918095 · doi:10.1063/1.2918095
[13] Weinstock R., Calculus of Variations (1952) · Zbl 0049.19503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.