Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces

We present a characterization for the rotational soliton for the curve shortening flow (CSF) on the revolution surfaces of \(\mathbb {R}^3\) ${\mathbb{R}}^3$ . Furthermore, we describe the behavior of such curves by showing that the two ends of each open curve are asymptotic to a parallel geodesic.