Binary differential equations at parabolic and umbilical points for\n 2-parameter families of surfaces

2017/08/16 by Jorge Luiz Deolindo Silva, Yutaro Kabata, Silva, Jorge Luiz Deolindo +3
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1708.04918

Abstract

We determine local topological types of binary differential equations of\nasymptotic curves at parabolic and flat umbilical points for generic\n2-parameter families of surfaces in mathbb P³ by comparing our projective\nclassification of Monge forms and classification of general BDE obtained by\nTari and Oliver. In particular, generic bifurcations of the parabolic curve are\nclassified. The flecnodal curve is also examined by direct computations, and we\npresent new bifurcation diagrams in typical examples.\n

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