Aeppli Cohomology and Gauduchon Metrics

Piovani, Riccardo; Томассини, Адриано

doi:10.1007/s11785-020-00984-6

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…A (M αβ ) = 1 (see the proof of [3,Theorem 3.3]) and that the Aeppli class of a pluriclosed Hermitian metric on a compact complex surface is non-zero (see e.g. [46]). Therefore, given any pluriclosed metric ω on M αβ one has [ω] = λ[ω Hopf ] for 0 < λ ∈ R, where the positivity of λ follows e.g.…”

Section: Bismut Hermitian-einstein Metricsmentioning

confidence: 99%

Non-Kähler Calabi-Yau geometry and pluriclosed flow

Garcia-Fernandez¹,

Jordan²,

Streets³

2021

Preprint

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Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independently in mathematical physics. We reinterpret this condition in terms of the Hermitian-Einstein equation on an associated holomorphic Courant algebroid, and thus refer to solutions as Bismut Hermitian-Einstein. This implies Mumford-Takemoto slope stability obstructions, and using these we exhibit infinitely many topologically distinct complex manifolds in every dimension with vanishing first Chern class which do not admit Bismut Hermitian-Einstein metrics. This reformulation also leads to a new description of pluriclosed flow in terms of Hermitian metrics on holomorphic Courant algebroids, implying new global existence results, in particular on all complex non-Kähler surfaces of Kodaira dimension κ ≥ 0. On complex manifolds which admit Bismut-flat metrics we show global existence and convergence of pluriclosed flow to a Bismut-flat metric, which in turn gives a classification of generalized Kähler structures on these spaces.

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Section: Bismut Hermitian-einstein Metricsmentioning

confidence: 99%

Non-Kähler Calabi-Yau geometry and pluriclosed flow

Garcia-Fernandez¹,

Jordan²,

Streets³

2021

Preprint

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“…In [14, p.467] it is proved that every left-invariant (2, 2)-form is d-exact (see also [15] for cohomological computations). Let us define a complex curve of almost complex structures on Γ\G through a basis of (1, 0) forms by setting…”

Section: Curves Of Almost Complex Structures Preserving the 2 Th -Powermentioning

confidence: 99%

Families of almost complex structures and transverse $(p,p)$-forms

Hind,

Medori,

Tomassini

2021

Preprint

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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 symplectic form for t = 0. Furthermore, examples of special compact nilmanifolds with and without almost p-Kähler structures are presented. Contents 1. Introduction 1 2. Almost p-Kähler structures 4 3. Curves of almost complex structures preserving the 2 th -power 6 4. Semi-Kähler deformations of balanced metrics 10 5. Applications and examples 13 References 19

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