Relaxed hyperelastic curves

Volume 102 / 2011

Ahmet Yücesan, Gözde Özkan, Yasemín Yay Annales Polonici Mathematici 102 (2011), 223-230 MSC: 53A04, 53A05, 53C22, 74B20. DOI: 10.4064/ap102-3-3


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.


  • Ahmet YücesanDepartment of Mathematics
    Süleyman Demirel University
    32260 Isparta, Turkey
  • Gözde ÖzkanSüleyman Demirel University
    Graduate School of Natural and Sciences
    Department of Mathematics
    Isparta, Turkey
  • Yasemín YayDepartment of Mathematics
    Giresun University
    28100 Giresun, Turkey

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