Geometry of bifurcation sets of generic unfoldings of corank two functions

2021/01/20 by Kentaro Saji, Samuel P. dos Santos, Saji, Kentaro +1
Mathematics · #53A05 #58K05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2101.07967

openalex publication_date 2021/01/20 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

Abstract

We study the geometry of bifurcation sets of generic unfoldings of D₄^±-functions. Taking blow-ups, we show each of the bifurcation sets of D₄^±-functions admit a parametrization as a surface in R³. Using this parametrization, we investigate the behavior of the Gaussian curvature and the principal curvatures. Furthermore, we investigate the number of ridge curves and subparabolic curves near their singular point.

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