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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-3,
author = {Ahmet Y\"ucesan and G\"ozde \"Ozkan and Yasem\'\i n Yay},
title = {Relaxed hyperelastic curves},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {223-230},
zbl = {1235.53002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-3}
}
Ahmet Yücesan; Gözde Özkan; Yasemín Yay. Relaxed hyperelastic curves. Annales Polonici Mathematici, Tome 101 (2011) pp. 223-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-3/