  In this paper we study warped-product metrics on manifolds of the form $X
\setminus Y$, where $X$ denotes either $\mathbb{H}^n$ or $\mathbb{C}
\mathbb{H}^n$, and $Y$ is a totally geodesic submanifold with arbitrary
codimension. The main results that we prove are curvature formulas for these
metrics on $X \setminus Y$ expressed in spherical coordinates about $Y$. We
also discuss past and potential future applications of these formulas.
