2024/10/09 by Samuel Blitz, Blitz, Samuel, Josef Šilhan +1
Mathematics · #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2410.06706
openalex publication_date 2024/10/09 · openalex created_date 2024/10/12 · openalex updated_date 2026/07/28
Warped products are one of the simplest families of Riemannian manifolds that can have non-trivial geometries. In this article, we characterize the geometry of hypersurface embeddings arising from warped product manifolds using the language of higher (Riemannian) fundamental forms. In a similar vein, we also study the geometry of conformal manifolds with embedded hypersurfaces that admits a trivialization of the conformal metric to a product metric, with base manifold given by the embedded hypersurface. We show that the higher conformal fundamental forms play a critical role in their characterization.