Soliton solution to the time-like curve shortening flow in the pseudo-sphere

Abstract

A time-like curve on the unit pseudo-sphere can be a solition solution to the time-like curve shortening flow We first introduce the sufficient conditions for it to hold. And by studying the properties of the structure function of non-geodesic curves, I deduce some conditions to be satisfied by the structure function of non-geodesic curves when forming the time-like space plane, and then analyze the influence of the extreme value point of the structure function, and finally discuss the classification according to the time-like space-like situation of the parameter vector.