The Geometry of Inextensible Flows of Timelike Curves according to Quasi Frame in Minkowski space $\mathbb{R}^{2,1}$

Abstract In this paper, we study the geometry of the motion of timelike curves by quasi-frame according to the velocity and acceleration fields in Minkowski space $\mathbb{R}^{2,1}$. We study the timelike curves and get sufficient conditions to be inextensible. Also, we obtain the explicit form of the evolution equations for quasi orthonormal vectors (tangent, quasi-normal, and quasi binormal) of the quasi-timelike curve and the evolution equations of the quasi curvatures as a system of partial differential equations. We give new applications to the motion of quasi-timelike curves according to quasi-frame by velocity fields and acceleration fields.Mathematics subject classification 2020: 53A04;53A05; 53E10; 53Z05.