Generalizing the Equal Area Zones Property of the Sphere

Abstract.

We construct and study n-dimensional hypersurfaces in (n + 1)-dimensional Euclidean space that satisfy a higher dimensional generalization of the equal area zones property of the sphere (that the surface area of a zone between two parallel planes depends only on the distance between the planes). These new hypersurfaces are hypersurfaces of revolution. The relative simplicity of their construction allows us to describe them in great detail, revealing some interesting curiosities and motivating further questions.