HYPERELASTIC CURVES ALONG IMMERSIONS

Şahin B., ÖZKAN TÜKEL G., TURHAN T.

Miskolc Mathematical Notes, cilt.22, sa.2, ss.915-927, 2021 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.18514/mmn.2021.3501
  • Dergi Adı: Miskolc Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.915-927
  • Anahtar Kelimeler: Hyperelastic curve, Isometric immersion, Mean curvature vector field, Riemannian manifold
  • Isparta Uygulamalı Bilimler Üniversitesi Adresli: Evet

Özet

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