The Gauss equations and rigidity of isometric embeddings

DOI10.1215/S0012-7094-83-05039-1zbMath0526.53018OpenAlexW2059304805MaRDI QIDQ594391

Eric Berger, Phillip A. Griffiths, Robert L. Bryant

Publication date: 1983

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-83-05039-1

zbMATH Keywords

isometric embeddingsrigidity theoremsGauss equationstheorem of Burstin-Cartan-Janet-Schaefly

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Local submanifolds (53B25)

Related Items

Compatibility equations for isometric embeddings of Riemannian manifolds, Minimal immersions, Einstein's equations and Mach's principle, Some extensions of Horrocks criterion to vector bundles on Grassmannians and quadrics, Bianchi's Bäcklund transformation for higher dimensional quadrics, Riemannian metrics on tangent bundles, Affine embeddings of flat compact manifolds. I, On isometric and minimal isometric embeddings, Isometric immersions of surfaces with two classes of metrics and negative Gauss curvature, The linearized system for isometric embeddings and its characteristic variety, Geometric, algebraic, and analytic descendants of Nash isometric embedding theorems, Isometric Euclidean embeddings of a compact manifold form a Fréchet manifold, Weak continuity of the Gauss-Codazzi-Ricci system for isometric embedding, The base space of a strongly parabolic Riemannian manifold, Bending of surfaces. III, Compatibility of Gauß maps with metrics, Local rigidity of hypersurfaces in real Euclidean spaces., Conformally isometric embeddings and Hawking temperature, Special geometry, Isometric embeddings of spherical spaceforms with cyclic fundamental groups, Finiteness of infinitesimal deformations and infinitesimal rigidity of hypersurfaces in real Euclidean spaces, Characteristics and existence of isometric embeddings, On the Gauss equation of an isometric immersion

Cites Work

• Faisceaux algébriques cohérents
• Characteristics and existence of isometric embeddings
• Rigidity for isometric imbeddings
• Sur l'existence d'immersions isometriques locales pour les variétés riemanniennes
• Local isometric imbedding of Riemannian \(n\)-manifolds into Euclidean \((n+1)\)-space
• Existence theorems for analytic linear partial differential equations
• Analytic isometric embeddings
• Factorization of Curvature Operators
• Some isometric embedding and rigidity results for Riemannian manifolds
• Rigidity for Spaces of Class Greater Than One
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