The contact Whitney sphere

Abstract

In this paper, we introduce the contact Whitney sphere as an imbedding of the n-dimensional unit sphere as an integral submanifold of the standard contact structure on R2n+1. We obtain a general inequality for integral submanifolds in R2n+1, involving both the scalar curvature and the mean curvature, and we use the equality case in order to characterize the contact Whitney sphere. We also study a similar problem for anti-invariant submanifolds of R2n+1, tangent to the structure vector field.