Research article

Geometry of curve flows in isotropic spaces

  • Received: 06 January 2020 Accepted: 26 March 2020 Published: 07 April 2020
  • MSC : 53B30, 53C40, 53Z05

  • 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.

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

    Related Papers:

  • 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 License (http://creativecommons.org/licenses/by/4.0)
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