I am trying to prove the theorem that:
Let $(M,g)$ be a Riemannian $n$-manifold of constant sectional curvature $C$. Then the curvature tensor is $R(X,Y)Z=C( \langle Y,Z \rangle X - \langle X, Z \rangle Y)$.
I can show by straight-forward calculation (using the definition of sectional curvature) that if the curvature tensor is as stated, then $M$ has constant sectional curvature.
But the other way around is giving me some trouble. Does anybody have a hint?