Riemannian manifolds with structure groupG 2

Fernández, Marisa; Gray, Alfred

doi:10.1007/bf01760975

Cited by 300 publications

(525 citation statements)

References 17 publications

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“…In a local frame this can be given by The adjoint representation of SO(7) decomposes as 21 → 7 + 14 where 14 is the adjoint representation of G 2 . The intrinsic torsion then decomposes into four modules [26],…”

Section: G-structures In Canonical Dimensionmentioning

confidence: 99%

Superstrings with intrinsic torsion

2004

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We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form Ê 1,9−d × M d , in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalised calibrations naturally appear since the geometries always admit NS or type I/heterotic fivebranes wrapping calibrated cycles.Some new solutions are presented. In particular we find d = 6 examples with a fibred structure which preserve N = 1, 2, 3 supersymmetry in type II and include compact type I/heterotic geometries.

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Section: G-structures In Canonical Dimensionmentioning

confidence: 99%

Superstrings with intrinsic torsion

2004

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“…[9,14,17]. They are Λ 3 1 Λ 3 7 Λ 3 27 , with the lower indices standing for the respective dimensions.…”

Section: The Characteristic Connectionmentioning

confidence: 99%

On the characteristic connection of gwistor space

Albuquerque

2013

Open Mathematics

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We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature and deduce the condition under which T c is ∇ c -parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged. MSC:53C10, 53C20, 53C25, 53C28Keywords: Einstein metric • gwistor space • Characteristic torsion • G 2 structure © Versita Sp. z o.o. Gwistor spaces with parallel characteristic torsion The purposeIt has now become clear that every oriented Riemannian 4-manifold M gives rise to a G 2 -twistor space, as well as its celebrated twistor space. The former was discovered in [5,6] and we shall start here by recalling how it was obtained. Often we abbreviate the name G 2 -twistor for gwistor, as suggested in [3].Given M as before, the G 2 -twistor space of M consists of a natural G 2 structure on the S 3 -bundle over M of unit tangent vectors SM = { ∈ T M : = 1}exclusively induced by the metric = · · and orientation. We shall describe the characteristic connection ∇ c of SM in the case where M is an Einstein manifold. This guarantees the gwistor structure is cocalibrated (an equivalent condition) *

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“…There are in fact a total of 16 torsion classes of G 2 structures, each of which places certain restrictions on dϕ or d * ϕ [11]. One of the most important classes of manifolds with G 2 structure are manifolds with G 2 holonomy.…”

Section: Overview Of G Structuresmentioning

confidence: 99%

“…The kinetic term for the s M appears from the reduction of the R (11) term in (4.45). This is less straightforward that the derivation of L kin (c), but the calculation was shown explicitly in [14].…”

Section: G 2 Manifolds In M-theorymentioning

confidence: 99%

Local Geometry of the G 2 Moduli Space

Grigorian¹,

Yau

2008

Commun. Math. Phys.

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We consider deformations of torsion-free G 2 structures, defined by the G 2 -invariant 3-form ϕ and compute the expansion of * ϕ to fourth order in the deformations of ϕ. By considering M -theory compactified on a G 2 manifold, the G 2 moduli space is naturally complexified, and we get a Kähler metric on it. Using the expansion of * ϕ we work out the full curvature of this metric and relate it to the Yukawa coupling.

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Riemannian manifolds with structure groupG 2

Cited by 300 publications

References 17 publications

Superstrings with intrinsic torsion

Superstrings with intrinsic torsion

On the characteristic connection of gwistor space

Local Geometry of the G 2 Moduli Space

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