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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© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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