The Riemannian metric g satisfies
g(P_X\,Y, W)=-g(Y, P_X\,W)
where P_X\,Y is denote tangential part of (\nabla_X\J)\,Y=P_X\,Y+Q_X\,Y.
that condition can we take on Nordan manifold?
Can you send me the condition of nordan manifold?
How to change S(X, Y)=S(J X, J Y) in index form, where J and S are complex structure and Ricci tensor.
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