Synge deduced some invariants with the property that when they arezero at a particular event of the spacetime then the curvature tensoris also zero at the same event. This almost unknown result of Syngeis used in this paper to show is importance. It is then applied toobtain conditions of immersion of R_4 into E_5, to generate theBel-Robinson tensor and to the Cauchy problem in geometrodynamics.
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