Differential equations and integral characterizations of timelike and spacelike spherical curves in the Minkowski space-time $E_1^4 $

In this paper we give differential equations characterizing timelike and spacelike curves lying on hyperbolic sphere $H_0^3 $ and Lorentzian sphere $S_1^3 $ in the Minkowski space-time $E_1^4 $. Furthermore, we give the integral characterizations of these curves in $E_1^4 $.