Let be given a manifold $M$, then we can consider the derivations over the exterior forms of degree $2k$ $\Lambda_+ (M)$:

$X(a \wedge b)=X(a) \wedge b+ a \wedge X(b)$

If $w$ is in $\Lambda_+ (M)$, we can define $w \wedge X$. The derivations are in isomorphism with $\Lambda_+ (M) \bigotimes TM$. The Koszul connection is:

i) $\nabla_X (w \wedge s)= X(w) \wedge s + w \wedge \nabla_X (s)$

ii) $ \nabla_{w \wedge X} (s)= w \wedge \nabla_X (s)$

We can define a riemannian metric: $g(X,Y)=g(Y,X)$ and $g(w \wedge X,Y)=w \wedge g(X,Y)$ with $X,Y$ two derivations. So we can define the Levi-Civita connection and the Riemann and Ricci curvature which are tensors over $M$. In this formalism, the Einstein equations for exterior forms seem to exist. Are they interesting in physics? Can we extend in supersymmetry to any exterior forms?