On the space-times admitting a synchronization of constant curvature

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Abstract
A synchronization S on the space-time is a foliation by spacelike hypersurfaces. We study here the vector fields, tangent to S, which are Killing fields for the induced metric on every instant of S but which are not necessarily Killing fields of the whole space-time metric; they are called S-Killing vector fields. We analyze the multiplicity of the maximal symmetry or complete integrability case, that is the case for which the space-times admit a synchronization S with the maximum number of S-Killing vector fields. In particular, the important case where S is umbilical is treated in detail.

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