Twistor and reflector spaces of almost para-quaternionic manifolds

Ivanov, Stefan; Minchev, Ivan; Zamkovoy, Simeon

doi:10.4171/079-1/14

Cited by 14 publications

(30 citation statements)

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“…However, if J and K are integrable, then also the almost paracomplex structure J • K is integrable, and in this case M, ω, J, K is called a hyper-para-Kähler manifold. Such manifolds are, for example, studied in the context of supersymmetry, see 13 . is widely used to study topological obstructions to the existence of symplectic forms on manifolds.…”

Section: Integrabilitymentioning

confidence: 99%

On Almost Hyper-Para-Kähler Manifolds

Merker

2012

ISRN Geometry

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In this paper it is shown that a 2n-dimensional almost symplectic manifold M, ω can be endowed with an almost paracomplex structure K, K Topological and metric properties of almost hyper-para-Kähler manifolds as well as integrability of J, K are discussed. It is especially shown that the Pontrjagin classes of the eigenbundles P ± of K to the eigenvalues ±1 depend only on the symplectic structure and not on the choice of K.

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Section: Integrabilitymentioning

confidence: 99%

On Almost Hyper-Para-Kähler Manifolds

Merker

2012

ISRN Geometry

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“…The theory of paraquaternionic manifolds has been developing in recent years ( [1], [5], [8], [9], [13]), although its roots date back to 50's, in the work of P. Libermann ([11]). …”

Section: Introductionmentioning

confidence: 99%

Submanifolds of an almost paraquaternionic Kahler product manifold

Vîlcu

2007

imf

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“…10) and(5.11) we deduce that (Φ 1 , V 1 , f 1 ) is an almost contact structure on M , while (Φ 2 , V 2 , f 2 ) and (Φ 3 , V 3 , f 3 ) are Lorentzian almost paracontact structures on M . Moreover, for α = β we have…”

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confidence: 99%