Let $(M,g)$ be a riemannian manifold with Riemann curvature $R$, I define a second sectional curvature:
$$K(X,Y,Z,T)=\frac{g(R(X,Y)X,Y)g(R(Z,T)Z,T)-g(R(X,Y)Z,T)^2}{g(X\wedge Y,X\wedge Y)g(Z\wedge T,Z\wedge T)-g(X\wedge Y,Z\wedge T)^2}$$
What are the manifolds with constant second sectional curvature?