Hypersurfaces with central convex cross-sections

2016/05/10 by Gur, Metin Alper
#52A20 #53A07 #53A15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.02862

Abstract

A hypersurface M in ℝⁿ, n ≥ 4, has central ovaloid property if M intersects some hyperplane transversally along an ovaloid and every such ovaloid on M has central symmetry. We show that a complete, connected, smooth hypersurface with central ovaloid property must either be a cylinder over a central ovaloid or else quadric.

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