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

2013/06/14 by Angelito Camacho Calderón, Calderón, Angelito Camacho, Adriana Ortiz Rodrí guez +1
Computer Science · Engineering · Mathematics · #53A05 #53A15 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1306.3483

openalex publication_date 2013/06/14 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

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

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