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• W3205121638 abstract "We consider curves $gamma : [0, 1]tomathbb{R}^3$ endowed with an adapted orthonormal frame $r : [0, 1]to SO(3)$. We are interested in the cases where the frame is constrained, in the sense that one of its `curvatures' (i.e., off-diagonal elements of $r'r^T$) is prescribed. One example is the Fr'enet frame. In order to deform such constrained framed curves without spoiling the constraint, we proceed in two stages. First we deform the frame $r$ in a way that is naturally compatible with the differential constraint, by interpreting it in terms of parallel transport on the sphere. The deformation of the base curve $gamma$ is achieved in a second step, by means of a suitable reparametrization of the frame. We illustrate this deformation procedure by providing some applications." @default.
• W3205121638 created "2021-10-25" @default.
• W3205121638 creator A5004316527 @default.
• W3205121638 date "2021-10-16" @default.
• W3205121638 modified "2023-09-27" @default.
• W3205121638 title "Deformation of Framed Curves" @default.
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