On D⁺_J operator on higher dimensional almost Kähler manifolds

2025/03/18 by Tan, Qiang, Wang, Hongyu, Wang, Ken
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.14101

Abstract

In this paper, we define D⁺_J operator that is a generalized ∂∂ operator on higher dimensional almost Kähler manifolds. In terms of D⁺_J operator, we study ∂-problem in almost Kähler geometry and the generalized Monge-Ampère equation on almost Kähler manifolds. Similarly to the Kähler case, we obtain C^∞ a priori estimates for the solution of the generalized Monge-Ampère equation on the almost Kähler manifold (M,ω,J) depended only on ω and J. Then as done in Kähler geometry, we study Calabi conjecture for almost Kähler manifolds. Finally, we will pose some questions in almost Kähler geometry.

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