Focal surfaces of fronts associated to unbounded principal curvatures

2022/10/12 by Keisuke Teramoto, Teramoto, Keisuke · 1 citation
Mathematics · Physics and Astronomy · #53A05 #53A55 #57R45 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2210.06221

openalex publication_date 2022/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near non-degenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of singularities and geometrical properties of initial fronts. Moreover, we investigate behavior of the Gaussian curvature of the focal surface.

Cited by

• Cuspidal edges on focal surfaces of regular surfaces with parabolic points

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