2023/11/25 by Toshizumi Fukui, Fukui, Toshizumi, Atsuki Hiramatsu +1
Engineering · Mathematics · #Advanced Materials and Mechanics #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2311.15140
openalex publication_date 2023/11/25 · openalex created_date 2023/11/29 · openalex updated_date 2026/07/28
We introduce the rotation unfolding of the folding map of a surface in ℝ3, and investigate its A-vesality. The rotation unfolding is a 2-parameter unfolding and can be considered as a subfamily of the folding family, which is introduced by Bruce and Wilkinson. They revealed relationships between a bifurcation set of this family and the focal/symmetry set of a surface in ℝ3. We state the criteria of singularities of the folding map up to codimension 2 and prove when our rotation unfolding is versal. The conditions to be versal are stated in terms of geometry. As a by-product, we show the diffeomorphic type of the locus of the tangent planes of the focal set of regular surfaces, which passes through the origin.