Geometry of curve flows in isotropic spaces

Gurbuz N., Yoon D. W.

AIMS MATHEMATICS, cilt.5, sa.4, ss.3434-3445, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3934/math.2020222
  • Dergi Adı: AIMS MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3434-3445
  • Anahtar Kelimeler: Hasimoto surface, Schrodinger flow, extended Harry-Dym flow, isotropic space, SOLITON
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

In this paper, we study inextensible flows of a curve in an isotropic 3-space and give a necessary and sufficient condition for inextensible flows of the curve as a partial differential equation involving the curvatures of the curve. Using binormal flows of a space curve we give the Backlund transformations of the Schrodinger flows and the extended Harry-Dym flows. Finally, we investigate some geometric properties of Hasimoto surfaces which wiped out by the Schrodinger flows.