Central cross-sections make surfaces of revolution quadric

2007/12/17 by Bruce Solomon, Solomon, Bruce
Computer Science · Mathematics · #53A05 #53A15 #Advanced Differential Equations and Dynamical Systems #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.0712.2796

openalex publication_date 2007/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove here that when all planes transverse and nearly perpendicular to the axis of a surface of revolution intersect it in loops having central symmetry, the surface must be quadric. It follows that the quadrics are the only surfaces of revolution without skewloops. Similar statements hold for hypersurfaces of revolution in higher dimensions.

Related

• Surfaces with central cross-sections
• Characterization of polynomial surfaces of revolution and polynomial quadrics
• Skew loops and quadric surfaces
• Central figure-8 cross-cuts make surfaces cylindrical
• Hypersurfaces with central convex cross-sections