Umbilic Singularities and Lines of Curvature on Ellipsoids of \mathbb R⁴

2014/05/11 by Débora Lopes, Lopes, Débora, Jorge Sotomayor +3
Mathematics · Physics and Astronomy · #37C15 #53C12 #57R30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG #math.DS #msc:37C15 #msc:53C12 #msc:57R30

paper · pdf · doi:10.48550/arxiv.1405.2537

31 pages and 12 figures

arxiv created 2014/05/11 · openalex publication_date 2014/05/11 · arxiv updated 2014/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The topological structure of the lines of principal curvature, the umbilic and partially umbilic singularities of all tridimensional ellipsoids of \mathbb R⁴ is described.

Related

• Partially umbilic singularities of hypersurfaces of \mathbb R⁴
• Lines of Curvature on Quadric Hypersurfaces of ℝ⁴
• On the Patterns of Principal Curvature Lines around a Curve of Umbilic Points
• Codimension two Umbilic points on Surfaces Immersed in R³
• Principal Mean Curvature Foliations on Surfaces immersed in \mathbb R ⁴