Euler-Lagrange formulas for pseudo-Kähler manifolds

Let c be a characteristic form of degree k which is defined on a Kähler manifold of real dimension m>2k. Taking the inner product with the Kähler form Ωk gives a scalar invariant which can be considered as a generalized Lovelock functional. The associated Euler-Lagrange equations are a generalized Einstein-Gauss-Bonnet gravity theory; this theory restricts to the canonical formalism if c=c2 is the second Chern form. We extend previous work studying these equations from the Kähler to the pseudo-Kähler setting.