Relaxed elastic line on a curved pseudo-hypersurface in pseudo-Euclidean spaces

In this work, we derive the Euler–Lagrange equation for an elastic line which is lying on a pseudo-hypersurface in pseudo-Euclidean spaces E ν n . Following this, we check the solutions which depend on the boundary conditions whether they are geodesic on a pseudo-hypersurface or not. The relaxed ela...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2006-03, Vol.315 (1), p.367-378
Main Authors: Çöken, A. Ceylan, Yücesan, Ahmet, Ayyildiz, Nihat, Manning, Gerald S.
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Differential geometry
Elasticity problem
Euler–Lagrange equations
Exact sciences and technology
Geodesics
Geometry
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Partial differential equations
Pseudo-Euclidean spaces
Pseudo-hypersurfaces
Relaxed elastic line
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this work, we derive the Euler–Lagrange equation for an elastic line which is lying on a pseudo-hypersurface in pseudo-Euclidean spaces E ν n . Following this, we check the solutions which depend on the boundary conditions whether they are geodesic on a pseudo-hypersurface or not. The relaxed elastic line on a pseudo-hyperplane, a pseudo-hypersphere, and pseudo-hyperbolic space is a geodesic. However, the relaxed elastic line on a pseudo-hypercylinder, is a space-like geodesic.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2005.05.051