Self-duality of neutral metrics on four-dimensional manifolds (Q2752838)

A neutral metric on an oriented four-manifold is said to be self-dual if its Weyl conformal tensor, regarded as an endomorphism on the space of 2-forms, is self-dual. NEWLINENEWLINENEWLINEThe author (i) recalls basic facts for self-duality of neutral metrics on four-manifolds, (ii) introduces some geometric structures relevant to neutral metrics, e.g., a neutral Kähler structure, a split-quaternion structure, and studies relations with self-duality of neutral metrics, (iii) gives some typical examples of both compact and non-compact four-manifolds with self-dual neutral metrics, and (iv) poses several open problems related to neutral metrics on four-manifolds. NEWLINENEWLINENEWLINEThe results obtained are closely related to results published in [\textit{J. Petean}, Commun. Math. Phys. 189, No. 1, 227-235 (1997; Zbl 0898.53046)] and [\textit{J. Cendan-Verdes, E. García-Río}, and \textit{M. E. Vázquez-Abal}, Riv. Mat. Univ. Parma, V. Ser. 3, 253-270 (1994; Zbl 0851.53021)].NEWLINENEWLINEFor the entire collection see [Zbl 0953.00035].