Cr-invariants for surfaces in 4-space

2018/07/30 by Jorge Luiz Deolindo Silva, Silva, Jorge Luiz Deolindo · 1 citation
Engineering · Mathematics · #53A05 #57R45 #58K05 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1807.11133

openalex publication_date 2018/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish cross-ratio invariants for surfaces in 4-space in an analogous way to Uribe-Vargas's work for surfaces in 3-space. We study the geometric locii of local and multi-local singularities of ortogonal projections of the surface. The cross-ratio invariants at P₃(c)-points are used to recover two moduli in the 4-jet of the projective parametrization of the surface and show the stable configurations of asymptotic curves.

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• On evolutoids of regular surfaces in Euclidean 3-space

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