Let (M,g,J) be a Kaehler manifold (∇J=J∇), let R(X,Y) be the riemannian curvature. I define:
Ricc(J)=∑iR(Jei,ei)
for an orthonormal basis (ei)
R(J)=JRicc(J)
r(J)=tr(R(J))
then I can define the Einstein-Kaehler equations:
R(J)ij−(1/2)r(J)gij=Tij
Can I reformulate the gravitation by means of these equations?