Saved in:
Bibliographic Details
Main Authors: Blitz, Samuel, Silhan, Josef
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.06706
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915469118668800
author Blitz, Samuel
Silhan, Josef
author_facet Blitz, Samuel
Silhan, Josef
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_06706
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Higher Fundamental Forms and Warped Product Hypersurfaces
Blitz, Samuel
Silhan, Josef
Differential Geometry
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.
title Higher Fundamental Forms and Warped Product Hypersurfaces
topic Differential Geometry
url https://arxiv.org/abs/2410.06706