Is it possible to reconstruct the curvature tensor from the sectional curvature in the semi-Riemannian case?
In Kuhnel's book there is a proof using $k(X,Y)=\left\langle R(X,Y)Y,Y\right\rangle$, but I don't know how to recover this map in the case that $(X,Y)$ spans a degenerate plane.
Is it necessary to recover this map? Someone can help me giving an indication how can I do it?