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Carvalho, Marcelo; Oliveira, M. W. de; Sigaud, Xavier

doi:10.1023/a:1025725618916

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…In particular, a four-dimensional hyper-symplectic structure is equivalent to an ASD and Ricci-flat neutral metric. For this reason, such structures have been used in string theory [42,30,33,3,31,10] and integrable systems [16,4,17].…”

Section: Hyper-symplectic Metrics Of Dimensionmentioning

confidence: 99%

“…Furthermore, in dimension 4, any hyper-symplectic structure underlies an anti-self-dual (ASD) and Ricci-flat neutral metric. For this reason such structures have been used in string theory [42,30,33,3,31,10,26] and integrable systems [16,4,17]. In fact, N = 2 superstring theory is considered in [42], and it is proved that the critical dimension of such a string is 4 and that the bosonic part of the N = 2 theory corresponds to self-dual (SD) metrics of signature (2,2).…”

Section: Introductionmentioning

confidence: 99%

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Bianchi type A hyper-symplectic and hyper-Kähler metrics in 4D

Andrés¹,

Fernández²,

Ivanov³

et al. 2011

Class. Quantum Grav.

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We present a simple explicit construction of hyper-Kähler and hyper-symplectic (also known as neutral hyper-Kähler or hyper-parakähler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kähler and hyper-symplectic structures in dimension four.In this section we recover some of the known hyper-Kähler metrics in dimension four. To this end, we lift the special structure on the non-Euclidean Bianchi type groups of class A to a hyper-Kähler metric on its product with (an interval in) the real line.

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Section: Hyper-symplectic Metrics Of Dimensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bianchi type A hyper-symplectic and hyper-Kähler metrics in 4D

Andrés¹,

Fernández²,

Ivanov³

et al. 2011

Class. Quantum Grav.

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Complex Product Structures and Affine Foliations

Andrada

2005

Ann Glob Anal Geom

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A complex product structure on a manifold is an appropriate combination of a complex structure and a product structure. The existence of such a structure determines many interesting properties of the underlying manifold, notably that the manifold admits a pair of complementary foliations whose leaves carry affine structures. This is due to the existence of a unique torsionfree connection which preserves both the complex and the product structure; this connection is not necessarily flat. We study the existence of complex product structures on tangent bundles of smooth manifolds, and we investigate the structure of manifolds admitting a complex product structure and a compatible hypersymplectic metric, showing that the foliations mentioned earlier are either symplectic or Lagrangian, depending on the symplectic form under consideration. Mathematics Subject Classifications (2000): primary: 53C15, 53C07; secondary: 53C50, 53C55.

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Cited by 2 publications

References 8 publications

Bianchi type A hyper-symplectic and hyper-Kähler metrics in 4D

Bianchi type A hyper-symplectic and hyper-Kähler metrics in 4D

Complex Product Structures and Affine Foliations

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