On the realization problem of plane real algebraic curves as Hessian curves

Abstract

The Hessian Topology is a subject having interesting relations with several areas, for instance, differential geometry, implicit differential equations, analysis and singularity theory. In this article we study the problem of realization of a real plane curve as the Hessian curve of a smooth function. The plane curves we consider are constituted either by only outer ovals or inner ovals. We prove that some of such curves are realizable as Hessian curves.