Warped product metrics on hyperbolic and complex hyperbolic manifolds

2023/07/28 by Barry Minemyer, Minemyer, Barry
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2307.15553

Abstract

In this paper we study warped-product metrics on manifolds of the form X ∖ Y, where X denotes either ℍⁿ or ℂ ℍⁿ, 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.

Related

• A note on doubly warped product spaces
• A survey on geometry of warped product submanifolds
• Relative radial mass and rigidity of some warped product manifolds
• A New Type Warped Product Metric in Contact Geometry
• On Rigidity of hypersurfaces with constant curvature functions in warped product manifolds