Lines of Curvature on Quadric Hypersurfaces of $ \mathbb{R}^4$

Jorge Sotomayor; Ronaldo Garcia

arxiv: 1509.08337 · v1 · pith:6J7HJPK4new · submitted 2015-09-28 · 🧮 math.DG · math.DS

Lines of Curvature on Quadric Hypersurfaces of mathbb{R}⁴

Jorge Sotomayor , Ronaldo Garcia This is my paper

classification 🧮 math.DG math.DS

keywords hypersurfacescompactcurvatureellipsoidalhyperboloidslinesmathbbquadric

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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 ${\mathbb R}^4$. 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.

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Lines of Curvature on Quadric Hypersurfaces of mathbb{R}⁴

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