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

Authors: Luis C. de Andrés, Marisa Fernández, Stefan Ivanov, José A. Santisteban, Luis Ugarte, Dimiter Vassilev

arXiv: 1102.1518v2 - DOI (math.DG)
Title changed, exposition and terminology clarified, final vesion to appear Class. Quant. Grav. This paper is an expanded version of sections 7 and 8 of arXiv:0903.1398
License: NONEXCLUSIVE-DISTRIB 1.0

Abstract: 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.

Submitted to arXiv on 08 Feb. 2011

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