A splitting theorem for higher order parallel immersions

DOI10.1090/S0002-9939-2011-11342-XzbMath1285.53046arXiv1103.1615OpenAlexW2062470351MaRDI QIDQ2845561

Ines Kath, Paul-Andi Nagy

Publication date: 2 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.1615

zbMATH Keywords

space formsplitting theoremsparallel immersions\(k\)-parallel immersionsflat normal bundlesflat spaces

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• The classification of hypersurfaces of a Euclidean space with parallel higher order fundamental form
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• Minimal immersions of Riemannian products into real space forms
• Symmetric submanifolds of Euclidean space
• On symmetric submanifolds of spaces of constant curvature
• Curvature tensors and covariant derivatives
• Immersions with parallel second fundamental form
• Isometric immersions of warped products
• Produkt-Zerlegung von Immersionen mit paralleler zweiter Fundamentalform
• Nonlocal Hamiltonian operators of hydrodynamic type with flat metrics, integrable hierarchies, and the associativity equations
• Isometric immersions of Riemannian products
• Semiparallel Submanifolds in Space Forms
• A THEOREM ON CURVATURE TENSOR FIELDS

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