The Cauchy problem in general relativity. III. On locally imbedding a family of null hypersurfaces

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Abstract
This paper is concerned with the problem of locally imbedding a null hypersurface in a Riemannian manifold. More precisely, on a one‐parameter family of null hypersurfaces, rigged by an arbitrary null vector field, in a four‐dimensional space–time manifold, a particular symmetric affine connection is used to derive the corresponding generalized Gauss–Codazzi equations. In addition, expressions are obtained for the projections of the Ricci tensor, which are relevant to the characteristic initial‐value problem of general relativity.

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