2021/10/16 by Hornung, Peter
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)
paper · doi:10.48550/arxiv.2110.08541
We consider curves γ: [0, 1]→ℝ3 endowed with an adapted orthonormal frame r : [0, 1]→ 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'rT) is prescribed. One example is the Frénet 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 γ is achieved in a second step, by means of a suitable reparametrization of the frame. We illustrate this deformation procedure by providing some applications.