The axial curvature for corank 1 singular surfaces

2019/11/20 by Raúl Oset Sinha, Kentaro Saji, Sinha, Raúl Oset +1
Mathematics · #53A05 #57R45 #58K05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1911.08823

openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For singular corank 1 surfaces in \mathbb R³ we introduce a distinguished normal vector called the axial vector. Using this vector and the curvature parabola we define a new type of curvature called the axial curvature, which generalizes the singular curvature for frontal type singularities. We then study contact properties of the surface with respect to the plane orthogonal to the axial vector and show how they are related to the axial curvature. Finally, for certain fold type singularities, we relate the axial curvature with the Gaussian curvature of an appropriate blow up.

Citations

• Relating second order geometry of manifolds through projections and normal sections

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