$R(X,Y)=\nabla_X\nabla_Y-\nabla_Y\nabla_X-\nabla_{[X,Y]}$ is the curvature with respect to the Levi-Civita connection $\nabla$ of a metric $g$ on a manifold $M$.
Define the Riemann curvature tensor by $\mathfrak{R}(X,Y,Z,W)=g(R(X,Y)W,Z)$. I can't show $\mathfrak{R}:\wedge^2 TM\rightarrow\wedge^2 T^*M$ (well-defined by Bianchi) is nondegenerate.
Please help. This is not homework. I don't even know where to start. Thanks.