An optimal inequality on locally strongly convex centroaffine hypersurfaces

Abstract

In this paper, we establish a general inequality for locally strongly convex centroaffine hypersurfaces in ${\mathbb{R}}^{n+1}$ involving the norm of the covariant derivatives of both the difference tensor $K$ and the Tchebychev vector field $T$. Our result is optimal in that, applying our recent classification for locally strongly convex centroaffine hypersurfaces with parallel cubic form in [4], we can completely classify the hypersurfaces which realize the equality case of the inequality.

11 pages

References in corpus (2)

• Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form
• Completeness of hyperbolic centroaffine hypersurfaces

Cited by in corpus (2)

• On product affine hyperspheres in ${\mathbb{R}}^{n+1}$
• Every centroaffine Tchebychev hyperovaloid is ellipsoid