Geometry of Affine Warped Product Hypersurfaces

The purpose of this article is the study of warped product manifolds which can be realized either as centroaffine or graph hypersurfaces in some affine space. First, we show that there exist many such realizations. Then we establish general optimal inequalities in terms of the warping function and the Tchebychev vector field for such affine hypersurfaces. We also investigate warped product affine hypersurfaces which verify the equality case of the inequalities. Several applications are also presented.