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

Details On the interdependency of the Gauss-Codazzi-Ricci equations of local isometric embedding On the interdependency of the Gauss-Codazzi-Ricci equations of local isometric embedding

Feb 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..139g&link_type=abstract

General Relativity and Gravitation, Volume 8, Issue 2, pp.139-145

Physics

5

Scientific paper

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.

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