Generic distance-squared mappings on plane curves

2018/01/04 by Shunsuke Ichiki, Ichiki, Shunsuke
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1801.01292

openalex publication_date 2018/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. In this paper, compositions of a given plane curve and generic distance-squared mappings on the plane into the plane are investigated from the viewpoint of stability.

Related

• Distance-squared mappings
• Generalized distance-squared mappings of the plane into the plane
• Preservation of immersed or injective properties by composing generic generalized distance-squared mappings
• Geometric interpretation of generalized distance-squared mappings of ℝ² into ℝ^ℓ (ℓ ≥ 3)
• Around distance-squared mappings