Warped product metrics on hyperbolic and complex hyperbolic manifolds

Abstract

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.