A generalization of Zakalyukin's lemma, and symmetries of surface singularities

2021/04/08 by Atsufumi Honda, Honda, Atsufumi, Kosuke Naokawa +7
Mathematics · #33C05 #53A10 #53A35 #53C42 #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.2104.03505

openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Zakalyukin's lemma asserts that the coincidence of the images of two wave front germs implies the right equivalence of corresponding map germs under a certain genericity assumption. The purpose of this paper is to give an improvement of this lemma for frontals. Moreover, we give several applications for singularities on surfaces.

Related

• The fundamental theorem for singular surfaces with limiting tangent planes
• The Topology of Surface Singularities
• Singularities of Frontal Surfaces
• Distance squared functions on singular surfaces parameterized by smooth maps A-equivalent to S_k, B_k, C_k and F₄
• Counting D₄ singularities in the image of a wave front