Lines of Curvature on Quadric Hypersurfaces of ℝ⁴

2015/09/28 by Sotomayor, Jorge, Garcia, Ronaldo
#37C15 #53C12 #57R30 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.08337

Abstract

Here are described the geometric structures of the lines of principal curvature and the partially umbilic singularities of the tridimensional non compact generic quadric hypersurfaces of \mathbb R⁴. This includes the ellipsoidal hyperboloids of one and two sheets and the toroidal hyperboloids. The present study complements the analysis of the compact ellipsoidal hypersurfaces carried out by D. Lopes, R. Garcia and J. Sotomayor.

Related

• Umbilic Singularities and Lines of Curvature on Ellipsoids of \mathbb R⁴
• Partially umbilic singularities of hypersurfaces of \mathbb R⁴
• Differential geometry of line of curvature on parametric hypersurfaces in 𝔼⁴
• Local geometry of surfaces in \mathbf R⁴
• A relation between the curvature ellipse and the curvature parabola