Geodesic
Relaxed hyperelastic curves
Ahmet Yücesan1 ; Gözde Özkan2 ; Yasemín Yay3
1Department of Mathematics Süleyman Demirel University 32260 Isparta, Turkey
2Süleyman Demirel University Graduate School of Natural and Sciences Department of Mathematics Isparta, Turkey
3Department of Mathematics Giresun University 28100 Giresun, Turkey
Annales Polonici Mathematici, Tome 102 (2011) no. 3, pp. 223-230
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $E^{3}$, 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.
DOI : 10.4064/ap102-3-3
Keywords: define relaxed hyperelastic curve which generalization relaxed elastic lines oriented surface three dimensional euclidean space derive intrinsic equations relaxed hyperelastic curve surface examining relaxed hyperelastic curves plane sphere cylinder geodesics relaxed hyperelastic curves plane sphere cylinder relaxed hyperelastic curves only special cases

Ahmet Yücesan  1   ; Gözde Özkan  2   ; Yasemín Yay  3

1 Department of Mathematics Süleyman Demirel University 32260 Isparta, Turkey
2 Süleyman Demirel University Graduate School of Natural and Sciences Department of Mathematics Isparta, Turkey
3 Department of Mathematics Giresun University 28100 Giresun, Turkey 
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Ahmet Yücesan; Gözde Özkan; Yasemín Yay. Relaxed hyperelastic curves. Annales Polonici Mathematici, Tome 102 (2011) no. 3, pp. 223-230. doi: 10.4064/ap102-3-3

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