Warped product metrics on hyperbolic and complex hyperbolic manifolds

Author:

Barry Minemyer

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Metric Geometry (math.MG)

journal:

date:

2023-07-27 16:00:00

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.

PDF: Warped product metrics on hyperbolic and complex hyperbolic manifolds.pdf