We relate certain universal curvature identities for Kähler manifolds to the Euler–Lagrange equations of the scalar invariants which are defined by pairing characteristic forms with powers of the Kähler form.
Peter B. GILKEY. JeongHyeong PARK. Kouei SEKIGAWA. "Universal curvature identities and Euler–Lagrange formulas for Kähler manifolds." J. Math. Soc. Japan 68 (2) 459 - 487, April, 2016. https://doi.org/10.2969/jmsj/06820459