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.
On Kodaira–Spencer’s problem on almost Hermitian 4-manifolds / Sillari, L.; Tomassini, A.. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - (2024). [10.1142/S0129167X24420035]
On Kodaira–Spencer’s problem on almost Hermitian 4-manifolds
Sillari L.;Tomassini A.
2024-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
