Warped product metrics on hyperbolic and complex hyperbolic manifolds

Minemyer, Barry

doi:10.2140/agt.2025.25.2905

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Warped product metrics on hyperbolic and complex hyperbolic manifolds

Barry Minemyer

Algebraic & Geometric Topology 25 (2025) 2905–2932

DOI: 10.2140/agt.2025.25.2905

Abstract

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

Keywords

complex hyperbolic space, hyperbolic space, totally geodesic submanifold, warped product metric, sectional curvature

Mathematical Subject Classification

Primary: 53C20, 53C35

Secondary: 53C56, 57R25

References

Publication

Received: 14 September 2023

Revised: 11 July 2024

Accepted: 12 August 2024

Published: 17 September 2025

Authors

Barry Minemyer
Department of Mathematics, Computer Science, and Digital Forensics Commonwealth University - Bloomsburg Bloomsburg, PA United States

Open Access made possible by participating institutions via Subscribe to Open.

Volume 25, issue 5 (2025)