Sectional curvature and the determination of the metric in space-time
The known result that the curvature tensor of a Lorentz manifold determines the metric (in almost all cases) uniquely, remains true, if one takes the sectional curvature instead. Theorem: If two Lorentzian metrics g and g' on M have the same sectional curvatures for all (non null) tangent two spaces, g and g' are conformally related to any region of non constant curvature and are equal to any subregion which is not conformally flat.
scientific article; zbMATH DE number 3850015
scientific article