The flow-curvature of plane parametrized curves

Authors : Mircea CRASMAREANU

Pages : 417-428

Doi:10.31801/cfsuasmas.1165123

View : 170 | Download : 56

Publication Date : 2023-06-23

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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