SELF-DUALITY OF METRICS OF TYPE (2, 2) ON FOUR-DIMENSIONAL MANIFOLDS

Abstract

We study self-duality of pseudo-Riemannian metrics of type (2, 2). We show correspondences between self-duality of Riemannian metrics and that of pseudo-Riemannian metrics of type (2, 2) under appropriate conditions. Moreover we give global constructions for four-dimensional manifolds with self-dual metrics of type (2, 2).