Annales Academiæ Scientiarum Fennicæ
Volumen 45, 2020, 325-342


Rui Albuquerque

Departamento de Matemática da Universidade de Évora
Centro de Investigação em Matemática e Aplicações
Rua Romão Ramalho, 59, 7000, Évora, Portugal; rpa 'at'

Abstract. We find a remarkable family of G2 structures defined on certain principal SO(3)-bundles P±M associated with any given oriented Riemannian 4-manifold M. Such structures are always cocalibrated. The study starts with a recast of the Singer–Thorpe equations of 4-dimensional geometry. These are applied to the Bryant–Salamon construction of complete G2-holonomy metrics on the vector bundle of self- or anti-self-dual 2-forms on M. We then discover new examples of that special holonomy on disk bundles over H4 and HC2, respectively, the real and complex hyperbolic space. Only in the end we present the new G2 structures on principal bundles.

2010 Mathematics Subject Classification: Primary 53C25, 53C38; Secondary 53C20, 53C28, 53C29.

Key words: Self-dual metric, calibration, holonomy, G2 structure.

Reference to this article: R. Albuquerque: Self-duality and associated parallel or cocalibrated G2 structures. Ann. Acad. Sci. Fenn. Math. 45 (2020), 325-342.

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