HYPERELASTIC CURVES ALONG IMMERSIONS

Şahin B., ÖZKAN TÜKEL G., TURHAN T.

Miskolc Mathematical Notes, vol.22, no.2, pp.915-927, 2021 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.18514/mmn.2021.3501
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.915-927
  • Keywords: Hyperelastic curve, Isometric immersion, Mean curvature vector field, Riemannian manifold
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

Hyperelastic curves in a Riemannian manifold are solutions of a constrained variational problem and characterized by Euler–Lagrange equations. We study the effect of hyperelasticcurves on the geometry of isometric immersions. We investigate the relation betweenhyperelastic curves and umbilical submanifolds and apply the results to analyze classical elasticcurves. The case of a Riemannian manifold with constant sectional curvature is also discussedand some applications are presented for illustrating the results