Weyl Representation of the Space-Time of the Vacuum C Metric when m =0

By using the imaginary Weyl coordinate method, the whole space-time of the vacuum C metric when m = 0 can be represented by the Weyl coordinate system. In addition, a revised transformation relation between Weyl and Minkowski coordinates has been introduced, and the whole space-time obtained by the Minkowski form of the metric can also be represented by Weyl coordinate system.