Total curvature of non-differentiable curves.
Gustavo Corach, Horacio Porta (1987)
Revista Matemática Iberoamericana
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Displaying similar documents to “On certain systems of curves in Riemannian space.”
Total curvature of non-differentiable curves.
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We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases. ...