On the interdependency of the GaussCodazziRicci equations of local isometric embedding
Abstract
The GaussCodazziRicci equations governing the local isometric embedding of Riemannian spacesV _{n} ⊂v_{n} (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 semiRiemannian spaces, of a result of R. Blum we obtain a number of theorems and corollaries expressing forV _{n} ⊂ V_{N} this interdependency of the GaussCodazziRicci equations. They form a generalization of previous results and are felt to be useful for the study of the geometrical properties of spacetime and its threedimensional space sections.
 Publication:

General Relativity and Gravitation
 Pub Date:
 February 1977
 DOI:
 10.1007/BF00770733
 Bibcode:
 1977GReGr...8..139G