AIMS Mathematics, 2020, 5(4): 3434-3445. doi: 10.3934/math.2020222.

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Geometry of curve flows in isotropic spaces

1 Department of Mathematics and Computer Science, Eskisehir Osmangazi University, Eskisehir, Turkey
2 Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Republic of Korea

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 Bäcklund transformations of the Schrödinger flows and the extended Harry-Dym flows. Finally, we investigate some geometric properties of Hasimoto surfaces which wiped out by the Schrödinger flows.
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Keywords Hasimoto surface; Schrödinger flow; extended Harry-Dym flow; isotropic space

Citation: Nevin Gürbüz, Dae Won Yoon. Geometry of curve flows in isotropic spaces. AIMS Mathematics, 2020, 5(4): 3434-3445. doi: 10.3934/math.2020222


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