On the Kodaira-Spencer's problem on almost Hermitian 4-manifolds

2023/12/19 by Lorenzo Sillari, Sillari, L., Адриано Томассини +1
Mathematics · #32Q60 #58A14 (Primary) 53C15 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2312.12366

openalex publication_date 2023/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1954, Hirzebruch reported a problem posed by Kodaira and Spencer: on compact almost complex manifolds, is the dimension h^p,q _∂ of the kernel of the Dolbeault Laplacian independent of the choice of almost Hermitian metric? In this paper, we review recent progresses on the original problem and we introduce a similar one: on compact almost complex manifolds, find a generalization of Bott-Chern and Aeppli numbers which is metric-independent. We find a solution to our problem valid on almost Kähler 4-manifolds.

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