Euler-Lagrange formulas for pseudo-Kaehler manifolds

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Let c be a characteristic form of degree k which is defined on a Kaehler manifold of real dimension m>2k. Taking the inner product with the Kaehler 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 Kaehler to the pseudo-Kaehler setting.