The classical elastic curves in a 3-dimensional indefmite-Riemannian manifold

Abazari N., YAYLI Y.

Journal of Applied Sciences, cilt.12, sa.12, ss.1303-1307, 2012 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 12
  • Basım Tarihi: 2012
  • Doi Numarası: 10.3923/jas.2012.1303.1307
  • Dergi Adı: Journal of Applied Sciences
  • Derginin Tarandığı İndeksler: Scopus, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Metadex, Pollution Abstracts, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1303-1307
  • Anahtar Kelimeler: Elastic curve, Indefinite-Riemannian manifold, Minimum principle, Spacelike, Timelke
  • Ankara Üniversitesi Adresli: Evet

Özet

In this study the mathematical idealization of the classical variational problem in 3-dimemional indefinite-Riemannian Manifolds is studied for the curve α which is timelke and spacelke, parameterized by the arc-length. The geodesic curvature and torsion of an elastic curve are evaluated if they exist as the solutions of the dfferential equatiom for all dfferent cases. Due to elastic curve definition, the minimum principle theorem is applied to elastic energy function which is defined as the integral of the squared geodesic curvature of the curve. © 2012 Asian Network for Scientific Information.