Geometry of Minimally Deformed Vortices and Domain Walls

Abstract

In this paper we consider relativistic models that contain in their spectra of solutions extended topological defects. We find the geometrical constrains that describe deformed vortices and domain walls of constant width. Analytical form of these solutions in co-moving coordinates is identical with analytical form of the appropriate static solutions in the laboratory Cartesian coordinates. The geometrical constrains presented in this report describe fully the shape and the evolution of the vortices and domain walls of constant width.