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arXiv · 2410.06706

Higher Fundamental Forms and Warped Product Hypersurfaces

Samuel Blitz·Josef Silhan
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Abstract

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.

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Samuel Blitz, Josef Silhan. 2024-10-09. Higher Fundamental Forms and Warped Product Hypersurfaces. https://arxiv.org/abs/2410.06706

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