Ovoidal hypersurface

Definition

A hypersurface in $\mathbb {R} ^{n}$ is said to be an ovoidal hypersurface if through every point in the hypersurface, there is a unique hyperplane that lies completely in the upper half-space corresponding to the point, and which intersects the hyperplane only at the point.

Equivalently an ovoidal hypersurface is a smooth and convex hypersurface.