Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions
Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions
Abstract We study the local geometry of 4-manifolds equipped with a para-Kähler-Einstein (pKE) metric, a special type of split-signature pseudo-Riemannian metric, and their associated twistor distribution , a rank 2 distribution on the 5-dimensional total space of the circle bundle of self-dual null 2-planes. For pKE metrics with non-zero scalar …