On symmetric submanifolds of spaces of constant curvature

DOI10.1007/BF01457052zbMath0499.53045OpenAlexW2095410135MaRDI QIDQ1171776

Erich Backes, Helmut Reckziegel

Publication date: 1983

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163758

zbMATH Keywords

Jordan triple systemsspaces of constant curvaturesymmetric submanifolds

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (18)

Locally symmetric immersions ⋮ Hypersurfaces with parallel Ricci tensor in spaces of constant curvature ⋮ The geometry generated on homogeneous spaces by morphisms of G-spaces ⋮ Isometric immersions of warped products ⋮ Submanifolds with semi-parallel Möbius second fundamental form in the unit sphere ⋮ Ric-semisymmetric submanifolds ⋮ A classification of pseudo-parallel hypersurfaces of \(\mathbb{S}^n \times \mathbb{R}\) and \(\mathbb{H}^n \times \mathbb{R}\) ⋮ Submanifolds with parallel Möbius second fundamental form in the unit sphere ⋮ Semi-parallel hypersurfaces of a real space form ⋮ COMPLETE CLASSIFICATION OF PARALLEL LORENTZIAN SURFACES IN LORENTZIAN COMPLEX SPACE FORMS ⋮ Higher order parallel surfaces in the Heisenberg group ⋮ Parallel submanifolds of the real 2-Grassmannian ⋮ Complete classification of parallel spatial surfaces in pseudo-Riemannian space forms with arbitrary index and dimension ⋮ Hypersurfaces with a parallel higher fundamental form ⋮ LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES ⋮ A splitting theorem for higher order parallel immersions ⋮ Geometric applications of Euclidean Jordan triple systems ⋮ On submanifolds with parallel Möbius second fundamental form in the unit sphere

Cites Work

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• A class of distinguished isometric immersions with parallel second fundamental form
• Geometric applications of Euclidean Jordan triple systems
• Symmetric submanifolds of Riemannian manifolds
• Symmetric submanifolds of Euclidean space
• Minimal imbeddings of R-spaces
• Untermannigfaltigkeiten mit paralleler zweiter Fundamentalform in Euklidischen Räumen und Sphären
• On the problem whether the image of a given differentiable map into Riemannian manifold is contained in a submanifold with parallel second fundamental form.
• Transformation Groups on Compact Symmetric Spaces

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