Hypersurfaces with central convex cross-sections

A hypersurface \(M\) in \(\mathbb{R}^n\), \(n \geq 4\), 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 eit...

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Bibliographic Details
Published in:arXiv.org 2016-05
Main Author: Metin Alper Gur
Format: Article
Language:English
Subjects:
Cylinders
Hyperplanes
Hyperspaces
Online Access:Get full text
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Summary:A hypersurface \(M\) in \(\mathbb{R}^n\), \(n \geq 4\), 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.
ISSN:2331-8422