- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 72 Issue: 2
- The flow-curvature of plane parametrized curves
The flow-curvature of plane parametrized curves
Authors : Mircea Crasmareanu
Pages : 417-428
Doi:10.31801/cfsuasmas.1165123
View : 159 | Download : 51
Publication Date : 2023-06-23
Article Type : Research Article
Abstract :We introduce and study a new frame and a new curvature function for a fixed parametrization of a plane curve. This new frame is called flow since it involves the time-dependent rotation of the usual Frenet flow; the angle of rotation is exactly the current parameter. The flow-curvature is calculated for several examples obtaining the logarithmic spirals (and the circle as limit case) and the Grim Reaper as flat-flow curves. A main result is that the scaling with$\\frac{1}{\\sqrt{2}}$ of both Frenet and flow-frame belong to the same fiber of the Hopf bundle. Moreover, the flow-Fermi-Walker derivative is defined and studied.Keywords : Plane parametrized curve, angular vector field, flow-frame, flow-curvature