We prove that the dimension h1,1 of the space of Dol-beault harmonic (1, 1)-forms is not necessarily always equal to b− ∂ on a compact almost complex 4-manifold endowed with an almost Hermitian metric which is not locally conformally almost Kähler. Indeed, we provide examples of non integrable, non locally con-formally almost Kähler, almost Hermitian structures on compact 4-manifolds with h1,1 = b−+1. This gives an answer to [6, Question ∂ 3.3] by Holt.
On the dimension of Dolbeault harmonic (1, 1)-forms on almost Hermitian 4-manifolds / Piovani, R.; Tomassini, A.. - In: PURE AND APPLIED MATHEMATICS QUARTERLY. - ISSN 1558-8599. - 18:3(2022), pp. 1187-1201. [10.4310/PAMQ.2022.v18.n3.a11]
On the dimension of Dolbeault harmonic (1, 1)-forms on almost Hermitian 4-manifolds
Piovani R.;Tomassini A.
2022-01-01
Abstract
We prove that the dimension h1,1 of the space of Dol-beault harmonic (1, 1)-forms is not necessarily always equal to b− ∂ on a compact almost complex 4-manifold endowed with an almost Hermitian metric which is not locally conformally almost Kähler. Indeed, we provide examples of non integrable, non locally con-formally almost Kähler, almost Hermitian structures on compact 4-manifolds with h1,1 = b−+1. This gives an answer to [6, Question ∂ 3.3] by Holt.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
