An explicit formula for Hessian potentials on warped product manifolds

We study Hessian geometry on warped product manifolds. In particular, we consider the case where the fiber space of the warped product is a Hessian manifold and the base space is an interval. For a given Hessian potential on the fiber space and some warping functions, we find an explicit formula for a Hessian potential and the affine coordinate systems on the warped product manifold. Moreover, we consider the obtained formula from the viewpoint of equiaffine differential geometry.