Bianchi type A hyper-symplectic and hyper-K\"ahler metrics in 4D

Dimiter Vassilev; Jos\'e A. Santisteban; Luis C. de Andr\'es; Luis Ugarte; Marisa Fern\'andez; Stefan Ivanov

arxiv: 1102.1518 · v2 · pith:YHGSN7K2new · submitted 2011-02-08 · 🧮 math.DG · hep-th

Bianchi type A hyper-symplectic and hyper-K\"ahler metrics in 4D

Luis C. de Andr\'es , Marisa Fern\'andez , Stefan Ivanov , Jos\'e A. Santisteban , Luis Ugarte , Dimiter Vassilev This is my paper

classification 🧮 math.DG hep-th

keywords hyper-kaehlerhyper-symplecticbianchiconstructionmetricstypeahlerclass

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We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-parakaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures in dimension four.

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Bianchi type A hyper-symplectic and hyper-K\"ahler metrics in 4D

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