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arXiv · 2307.15553

Warped product metrics on hyperbolic and complex hyperbolic manifolds

Barry Minemyer
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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.

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Barry Minemyer. 2023-07-28. Warped product metrics on hyperbolic and complex hyperbolic manifolds. https://doi.org/10.2140/agt.2025.25.2905

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