New HKT manifolds arising from quaternionic representations

Barberis, M. L.; Fino, Anna

doi:10.1007/s00209-009-0643-3

Cited by 15 publications

(23 citation statements)

References 39 publications

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“…dω r = 0 for any r = 1, 2, 3, then by Corollary 4 we get a strong HKT structure. An example in this case is given in [4,13].…”

Section: Corollarymentioning

confidence: 99%

“…for which the three Bismut connections associated to the three Hermitian structures (J r , h), r = 1, 2, 3, coincide. This geometry was introduced by Howe and Papadopoulos [21] and later studied for instance in [16,14,3,4,33]. Hyper-Hermitian connections with totally skew-symmetric torsion have applications in many branches of theoretical and mathematical physics.…”

Section: Introductionmentioning

confidence: 99%

“…Non-homogeneous examples of compact HKT manifolds have been constructed in [35] by considering the total space of a hyperholomorphic bundle over an HKT manifold. Other examples have been for instance constructed in [4] by using quaternionic representations and in [33] via the twist.…”

Section: Introductionmentioning

confidence: 99%

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HKT structures from almost contact manifolds

Fernández¹,

Fino²,

Ugarte³

et al. 2011

AIP Conference Proceedings

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A toric varieties approach to geometrical structure of multi partite states AIP Conf.A geometric approach to scalar field theories on the supersphere Abstract. We review some results on hyper-Kähler with torsion (HKT) structures on the total space of an S 1 -bundle over manifolds with three almost contact structures. Moreover, we show that deforming slightly the metric on the S 1 -bundle one may obtain an HKT structure starting from a 3-Sasakian structure, which allows us to construct examples of HKT structures from a 3-Sasakian structure on a certain Aloff-Wallach space.

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“…dω r = 0 for any r = 1, 2, 3, then by Corollary 4 we get a strong HKT structure. An example in this case is given in [4,13].…”

Section: Corollarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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HKT structures from almost contact manifolds

Fernández¹,

Fino²,

Ugarte³

et al. 2011

AIP Conference Proceedings

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“…The strong condition is that a certain three-form is closed. Very few examples of such structures are known that are not hyperKähler: following work of Joyce [23], and building on Spindel et al [32], Grantcharov and Poon [16] showed that bi-invariant metrics on most compact groups of dimension 4n are strong ; Barberis and Fino [6] produced other compact examples; otherwise most known examples, including those in [14], are incomplete. We show that starting with a hyperKähler manifold with circle symmetry, harmonic functions again govern which twists are strong .…”

Section: Introductionmentioning

confidence: 99%

Twists versus modifications

Swann

2016

Advances in Mathematics

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The twist construction is a geometric T-duality that produces new manifolds from old, works well with for example hypercomplex structures and is easily inverted. It tends to destroy properties such as the hyperKähler condition. On the other hand modifications preserve the hyperKähler property, but do not have an obvious inversion. In this paper we show how elementary deformations provide a link between the two constructions, and use the twist construction to build hyperKähler and strong HKT structures. In the process, we provide a full classification of complete hyperKähler four-manifolds with tri-Hamiltonian symmetry and study a number singular phenomena in detail.

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“…This connection is said to be an HKT-connection. This geometry is introduced in [25] and later studied for instance in [16,9,2,3,39]. A case of particular interest is when the torsion 3-form of such HKT-connection is closed.…”

Section: Introductionmentioning

confidence: 99%

A Connection With Parallel Totally Skew-Symmetric Torsion on a Class of Almost Hypercomplex Manifolds With Hermitian and Anti-Hermitian Metrics

Manev

Gribachev

2011

Int. J. Geom. Methods Mod. Phys.

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The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skewsymmetric. The class of the nearly Kähler manifolds with respect to the first almost complex structure is of special interest. It is proved that D has a D-parallel torsion and is weak if it is not flat. Some curvature properties of these manifolds are studied. Int. J. Geom. Methods Mod. Phys. 2011.08:115-131. Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 03/11/15. For personal use only. The almost (H, G)-manifoldsLet (M, H) be an almost hypercomplex manifold, i.e. M is a 4n-dimensional differentiable manifold and H = (J 1 , J 2 , J 3 ) is a triple of almost complex structures with the properties:for all cyclic permutations (α, β, γ) of (1, 2, 3) and I denotes the identity ([6, 1]). The standard structure of H on a 4n-dimensional vector space with a basis {X 4k+1 , X 4k+2 , X 4k+3 , X 4k+4 } k=0,1,...,n−1 has the form [37]:Further, x, y, z, w will stand for arbitrary differentiable vector fields on M . Let g be a pseudo-Riemannian metric on (M, H) with the properties

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New HKT manifolds arising from quaternionic representations

Cited by 15 publications

References 39 publications

HKT structures from almost contact manifolds

HKT structures from almost contact manifolds

Twists versus modifications

A Connection With Parallel Totally Skew-Symmetric Torsion on a Class of Almost Hypercomplex Manifolds With Hermitian and Anti-Hermitian Metrics

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