Hedgehogs and area of order 2

摘要

We define an algebraic area of order 2 for hedgehogs (envelopes parametrized by their Gauss map) in E~(n+1). On the vector space of hedgehogs defined up to a translation, this yields a nondegenerate quadratic form that allows us to define a scalar product on some subspaces, such as the subspace of projective hedgehogs. As an application, we give some characterizations of spheres among all convex hedgehogs of constant width.