Evolving Surfaces and Evolving Implicit Differential Equations Via Contact Geometry and Singularities

2020/08/03 by Ricardo Uribe-Vargas, Uribe-Vargas, Ricardo · 1 citation
Mathematics · Engineering · #Geometric Analysis and Curvature Flows #Material Science and Thermodynamics

paper · pdf · doi:10.48550/arxiv.2008.00967

Abstract

We present the list of unavoidable local phenomena (transitions) occurring on the configuration of the parabolic and flecnodal curves of evolving smooth surfaces in R³ (or RP³). We also present the list of transitions occurring on the curve of inflections of the solutions of evolving implicit differential equations (IDE). Our results are based on the properties of the contours of surfaces (in a contact 3-space) for projections all whose fibres are Legendrian. Keywords: Surface, flecnodal curve, contact geometry, implicit differential equations.

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