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