Relaxed hyperelastic curves
Volume 102 / 2011
Annales Polonici Mathematici 102 (2011), 223-230
MSC: 53A04, 53A05, 53C22, 74B20.
DOI: 10.4064/ap102-3-3
Abstract
We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space $E^{3}$, 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.
