Local geometry of surfaces in \mathbf R⁴

2013/04/08 by J. Basto-Gonçalves, Basto-Gonçalves, J.
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical and Theoretical Analysis #Mathematics and Applications #math.DG

paper · pdf · doi:10.48550/arxiv.1304.2242

arxiv created 2013/04/08 · openalex publication_date 2013/04/08 · arxiv updated 2013/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The indicatrix or curvature ellipse and the characteristic curve of a surface in \mathbf R⁴ are presented, as well as the projective duality connecting them. The characterisation of points in the surfaces as elliptic, parabolic and hyperbolic points, and the inflection points, are also discussed.

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