A Bonnet theorem for isometric immersions into products of space forms

DOI10.1007/S00013-010-0183-4zbMath1208.53061OpenAlexW2058613417WikidataQ125595960 ScholiaQ125595960MaRDI QIDQ607709

Sumit K. Garg

Publication date: 3 December 2010

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-010-0183-4

zbMATH Keywords

vector bundleGauss equationCodazzi equationRicci equation

Mathematics Subject Classification ID

Global submanifolds (53C40) Local submanifolds (53B25)

Related Items (14)

Spinorial representation of submanifolds in a product of space forms ⋮ Minimal Kähler submanifolds in product of space forms ⋮ On Hopf hypersurfaces of \(\mathbb{S}^2 \times \mathbb{S}^2\) and \(\mathbb{H}^2 \times \mathbb{H}^2\) ⋮ On Isometric Immersions of Null Manifolds into Semi-Riemannian Space Forms of Arbitrary Index ⋮ Isometric immersions into products of space forms ⋮ A fundamental theorem for submanifolds of multiproducts of real space forms ⋮ Biconservative submanifolds in \(\mathbb {S}^n\times \mathbb {R}\) and \(\mathbb {H}^n\times \mathbb {R}\) ⋮ Isometric immersions of higher codimension into the product \(S^k {\times} H^{n+p-k}\) ⋮ Minimal immersions of Riemannian manifolds in products of space forms ⋮ CMC biconservative surfaces in \(\mathbb S^n\times\mathbb R\) and \(\mathbb H^n\times\mathbb R\) ⋮ A Bonnet theorem for submanifolds into rotational hypersurfaces ⋮ A fundamental theorem for submanifolds in semi-Riemannian warped products ⋮ Characterization of hypersurfaces in four-dimensional product spaces via two different \(\text{Spin}^{\text{c}}\) structures ⋮ Ricci curvature on warped product submanifolds in spheres with geometric applications

Cites Work

• Unnamed Item
• Bending of surfaces. III
• Isometric immersions into products of space forms
• The imbedding of Riemann spaces in the large
• An existence theorem for $G$-structure preserving affine immersions
• Isometric immersions into $\mathbb {S}^n\times \mathbb {R}$ and $\mathbb {H}^n\times \mathbb {R}$ and applications to minimal surfaces
• On isometric immersions of Riemannian manifolds in euclidean space

This page was built for publication: A Bonnet theorem for isometric immersions into products of space forms