Relaxed hyperelastic curves

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YÜCESAN A. , Ozkan G. , Yay Y.

ANNALES POLONICI MATHEMATICI, vol.102, no.3, pp.223-230, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 102 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.4064/ap102-3-3
  • Title of Journal : ANNALES POLONICI MATHEMATICI
  • Page Numbers: pp.223-230

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.