Geometry of curve flows in isotropic spaces
AIMS MATHEMATICS, vol.5, no.4, pp.3434-3445, 2020 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 5 Issue: 4
- Publication Date: 2020
- Doi Number: 10.3934/math.2020222
- Journal Name: AIMS MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.3434-3445
- Keywords: Hasimoto surface, Schrodinger flow, extended Harry-Dym flow, isotropic space, SOLITON
- Eskisehir Osmangazi University Affiliated: Yes
Abstract
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.