Relative radial mass and rigidity of some warped product manifolds

2008/02/22 by Marc Arcostanzo, Arcostanzo, Marc, Erwann Delay +1
Mathematics · #53C21 #53C24 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · doi:10.48550/arxiv.0802.3270

openalex publication_date 2008/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a Riccati type formula adapted for two metrics having the same geodesics rays starting from a point or orthogonal to an hypersurface, one of these metrics being a warped product if the dimension n is greater than or equal to 3. This formula has non-trivial geometric consequences such as a positive mass type theorem and other rigidity results. We also apply our result to some standard models.

Citations

• A new proof of the positive energy theorem
• Manifolds with A Lower Ricci Curvature Bound

Related

• Warped product rigidity
• Warped products and synthetic lower curvature bounds: an overview
• Warped product metrics on hyperbolic and complex hyperbolic manifolds
• On Rigidity of hypersurfaces with constant curvature functions in warped product manifolds
• Some scalar curvature warped product splitting theorems