2025/08/10 by Yi Hu, Hu, Yi, Xiangsheng Wang +1
Mathematics · Physics and Astronomy · #14L24 #53D20 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2508.07168
openalex publication_date 2025/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we introduce the concept of momentumly closed forms. A non-degenerate momentumly closed two-form and its generalized moment map are the generalization of two well-known notions, symplectic forms and moment maps, in the almost Hermitian setting. We then generalize the classical theory of moment maps to this broader framework. As a first step, we prove a variant of the Darboux-Weinstein theorem for non-degenerate momentumly closed two-forms. Based on this, we further establish the convexity property of the generalized moment map, construct the corresponding reduction space and investigate the properties of the Kirwan-Ness stratification.