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On the interdependency of the Gauss-Codazzi-Ricci equations of local isometric embedding (1977)

Goenner, Hubert F.

Springer

General relativity and gravitation 8 (1977), S. 139-145

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ISSN: 1572-9532

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract The Gauss-Codazzi-Ricci equations governing the local isometric embedding of Riemannian spacesV n ⊂vn (N=n + P, P 〉 0) are interrelated by the Bianchi identities inV n andV N. This leads to redundancies which permit great simplification in the embedding problem, i.e. allows a neglect of part of the equations. By transcription, to the case of semi-Riemannian spaces, of a result of R. Blum we obtain a number of theorems and corollaries expressing forV n ⊂ VN this interdependency of the Gauss-Codazzi-Ricci equations. They form a generalization of previous results and are felt to be useful for the study of the geometrical properties of space-time and its three-dimensional space sections.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00770733

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