Coupled SU(3)-Structures and Supersymmetry

Fino, Anna; Raffero, Alberto

doi:10.3390/sym7020625

Cited by 12 publications

(11 citation statements)

References 36 publications

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“…It is also worth pointing out that this SU(3)-structure is half-flat cf. [12,18] and as such can be evolved by the Hitchin flow to construct a torsion-free G 2 -structure. The resulting metric belongs to the general class of metrics of the form ∧ Ω ± = 0 and 2…”

Section: Remarks On the Induced Su(3)-structure On ℂℙmentioning

confidence: 99%

$$S^1$$-quotient of Spin(7)-structures

Fowdar

2020

Ann Glob Anal Geom

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If a Spin(7)-manifold N 8 admits a free S 1 action preserving the fundamental 4-form, then the quotient space M 7 is naturally endowed with a G 2-structure. We derive equations relating the intrinsic torsion of the Spin(7)-structure to that of the G 2-structure together with the additional data of a Higgs field and the curvature of the S 1-bundle; this can be interpreted as a Gibbons-Hawking-type ansatz for Spin(7)-structures. In particular, we show that if N is a Spin(7)-manifold, then M cannot have holonomy contained in G 2 unless the N is in fact a Calabi-Yau fourfold and M is the product of a Calabi-Yau threefold and an interval. By inverting this construction, we give examples of SU(4) holonomy metrics starting from torsion-free SU(3)-structures. We also derive a new formula for the Ricci curvature of Spin(7)-structures in terms of the torsion forms. We then describe this S 1-quotient construction in detail on the Bryant-Salamon Spin(7) metric on the spinor bundle of S 4 and on flat ℝ 8 .

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Section: Remarks On the Induced Su(3)-structure On ℂℙmentioning

confidence: 99%

$$S^1$$-quotient of Spin(7)-structures

Fowdar

2020

Ann Glob Anal Geom

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“…, e 6 }, namely 4 ψ with |w 2 | constant (see e.g. [20]). Furthermore, on the nilpotent Lie algebra n 1 there are no coupled SU(3)-structures satisfying this condition (cf.…”

Section: Theorem 43 ([22]mentioning

confidence: 99%

“…Furthermore, on the nilpotent Lie algebra n 1 there are no coupled SU(3)-structures satisfying this condition (cf. [20,Prop. 12]).…”

Section: Theorem 43 ([22]mentioning

confidence: 99%

Recent results on closed G$_2$-structures

Fino¹,

Raffero²

2020

Preprint

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“…The main result of this section is the following Theorem 5.2. A nilmanifold M = Γ\G has an invariant mean convex half-flat structure if and only if the Lie algebra g of G is isomorphic to any of the Lie algebras g i , i = 6, 7, 8, 10, 13,15,16,22,24,25,28,29,30,31,32,33, as listed in Table 1.…”

Section: Mean Convex Half-flat Structures On Nilmanifoldsmentioning

confidence: 99%

Closed $\text{SL}(3,\mathbb{C})$-structures on nilmanifolds

Fino,

Salvatore

2020

Preprint

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A closed SL(3, C)-structure on an oriented 6-manifold is given by a closed definite 3-form ρ. In this paper we study two special types of closed SL(3, C)-structures. First we consider closed SL(3, C)-structures ρ which are mean convex, i.e. such that d(Jρρ) is a semi-positive (2, 2)-form, where Jρ denotes the induced almost complex structure. This notion was introduced by Donaldson in relation to G2-manifolds with boundary and as a generalization of nearly-Kähler structures. In particular, we classify nilmanifolds which carry an invariant mean convex closed SL(3, C)-structure. A classification of nilmanifolds admitting invariant mean convex half-flat SU(3)-structures is also given and the behaviour with respect to the Hitchin flow equations is studied. Then we examine closed SL(3, C)structures which are tamed by a symplectic form Ω, i.e. such that Ω(X, JρX) > 0 for each non-zero vector field X. In particular, we show that if a solvmanifold admits an invariant tamed closed SL(3, C)-structure, then it has also an invariant symplectic half-flat SU(3)-structure.

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Coupled SU(3)-Structures and Supersymmetry

Cited by 12 publications

References 36 publications

$$S^1$$-quotient of Spin(7)-structures

$$S^1$$-quotient of Spin(7)-structures

Recent results on closed G$_2$-structures

Closed $\text{SL}(3,\mathbb{C})$-structures on nilmanifolds

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