Projections from surfaces of revolution in the Euclidean plane

Abstract

In this paper, we determine the class of surfaces of revolution S for which there exists a smooth map $$\Phi $$ from a neighbourhood U of S to the Euclidean plane $$E^{2}$$ preserving distances infinitesimally along the meridians and the parallels of S and sending the meridional arcs of $$U\cap S$$ to straight lines of $$E^{2}$$ .