  In this paper, we prove a dihedral extremality and rigidity theorem for a
large class of codimension zero submanifolds with polyhedral boundary in warped
product manifolds. We remark that the spaces considered in this paper are not
necessarily warped product manifolds themselves. In particular, the results of
this paper are applicable to submanifolds (of warped product manifolds) with
faces that are neither orthogonal nor parallel to the radial direction of the
warped product metric. Generally speaking, the dihedral rigidity results
require the leaf of the underlying warped space to have positive Ricci
curvature and the warping function to be strictly log-concave. Nevertheless, we
prove a dihedral rigidity theorem for a large class of hyperbolic polyhedra,
where the leaf of the underlying warped product space is flat and the warping
function is not strictly log-concave.
