Energy functionals on almost Kähler manifolds: I

In this paper, we consider the Donaldson gauge functional and the twisted Aubin functionals on almost Kähler manifolds. As in Kähler geometry, we generalize the inequality between Aubin functionals.

💡 Research Summary

The paper investigates energy functionals on almost Kähler manifolds, extending several fundamental constructions from Kähler geometry to the non‑integrable setting. After a brief motivation, the authors introduce the basic differential operators that are adapted to an almost complex structure (J). The space of 2‑forms splits into (J)-invariant and (J)-anti‑invariant parts, denoted (\Omega^{+J}) and (\Omega^{-J}). Projections (P_{\pm J}) give rise to operators (d^{\pm J}=P_{\pm J}d) and their adjoints (d^{-J}d^{*}). Building on work of Lejmi and Tan‑et‑al., they define the crucial second‑order operator \