On the Twistor Theory of Almost-Grassmannian Manifolds

Abstract

In this document we present a twistor correspondence for half-flat almost-Grassmannian structures on real and complex manifolds. We provide foundational results regarding local theory in the complex setting and a global correspondence when the underlying manifold is a real Grassmannian of 2-planes. Whereas twistor constructions typically involve moduli of closed curves in a complex manifold, we utilize and expand upon the more flexible approach pioneered by LeBrun and Mason using moduli of curves-with-boundary.