Euler-Lagrange formulas for pseudo-Kaehler manifolds

TL;DR

This paper extends the study of Euler-Lagrange equations derived from characteristic forms on Kähler manifolds to the pseudo-Kähler setting, linking geometric invariants with generalized gravity theories.

Contribution

It generalizes previous work by extending Euler-Lagrange formulas from Kähler to pseudo-Kähler manifolds, broadening the scope of geometric and physical applications.

Findings

Derived Euler-Lagrange equations for pseudo-Kähler manifolds.

Connected characteristic forms to generalized Lovelock functionals.

Extended the canonical formalism to pseudo-Kähler geometry.

Abstract

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 $\Omega^k$ 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 $c=c_2$ is the second Chern form. We extend previous work studying these equations from the Kaehler to the pseudo-Kaehler setting.