The explicit general solution of trivial Monge-Ampère equation

Abstract

The general solution of the equation $z_{xx}{z}_{yy}-z_{xy}^2=0$ with minimal smoothness requirements is presented in explicit form; it depends on 2 functions of one variable. In particular, it allows to describe explicitly all developable surfaces (without planar points) in ${\mathbb{R}}^3$ . The domain and singularities of the solution are investigated.