2021
DOI: 10.48550/arxiv.2109.10939
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Families of almost complex structures and transverse $(p,p)$-forms

Richard Hind,
Costantino Medori,
Adriano Tomassini

Abstract: An almost p-Kähler manifold is a triple (M, J, Ω), where (M, J) is an almost complex manifold of real dimension 2n and Ω is a closed real tranverse (p, p)-form on (M, J), where 1 ≤ p ≤ n. When J is integrable, almost p-Kähler manifolds are called p-Kähler manifolds. We produce families of almost p-Kähler structures (Jt, Ωt) on C 3 , C 4 , and on the real torus T 6 , arising as deformations of Kähler structures (J0, g0, ω0), such that the almost complex structures Jt cannot be locally compatible with any symple… Show more

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Cited by 2 publications
(3 citation statements)
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“…Recently, their behaviour under small deformations of the complex structure has been studied in [19]. In [13] such forms have been extended to nonintegrable almost-complex manifolds and we recall here the following lemma that provides an obstruction to their existence, see [13,Proposition 3.4].…”
Section: P-kähler Structuresmentioning
confidence: 99%
See 1 more Smart Citation
“…Recently, their behaviour under small deformations of the complex structure has been studied in [19]. In [13] such forms have been extended to nonintegrable almost-complex manifolds and we recall here the following lemma that provides an obstruction to their existence, see [13,Proposition 3.4].…”
Section: P-kähler Structuresmentioning
confidence: 99%
“…Lemma 2.2 [13] Let (X , J ) be a compact complex manifold of complex dimension n. Suppose that there exists a non-closed (2n…”
Section: P-kähler Structuresmentioning
confidence: 99%
“…Recently, their behaviour under small deformations of the complex structure has been studied in [17]. In [11] such forms have been extended to nonintegrable almost-complex manifolds and we recall here the following lemma that provides an obstruction to their existence, see [11,Proposition 3.4].…”
Section: Introductionmentioning
confidence: 99%