Height functions on Whitney umbrellas

2012/05/14 by Toshizumi Fukui, Fukui, Toshizumi, Masaru Hasegawa +1 · 1 citation
Decision Sciences · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Topology and Set Theory #Differential Geometry (math.DG) #FOS: Mathematics #Fuzzy and Soft Set Theory #math.DG

paper · pdf · doi:10.48550/arxiv.1205.3044

openalex publication_date 2012/05/14 · arxiv created 2012/12/07 · arxiv updated 2012/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the singularities of the members of the family of height functions on Whitney umbrellas, which is also known as cross-caps, and show that the family of the height functions is a versal unfolding. Moreover, we study local intersections of a Whitney umbrella with a hyperplane through its singular point.

Citations

• The general type of singularity of a set of 2n−1 smooth functions of n variables

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• Behavior of Gaussian curvature and mean curvature near non-degenerate singular points on wave fronts

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