Hypersurfaces with central convex cross-sections

10 May 2016  ·  Gur Metin Alper ·

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...

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Differential Geometry Analysis of PDEs