Curvature characterizations of twistor spaces over four-dimensional Riemannian manifolds

Abstract

In this paper, we study the complex contact structure of a twistor space over a selfdual, Einstein 4-manifold with nonzero scalar curvature. Although the existence of such a structure has been known and well utilized by researchers for several decades now, the Hermitian geometry resulting from the complex contact structure is still in the process of being fully developed. Here we give a characterization of such twistor spaces as those satisfying a curvature (and hence purely geometric) identity. Later, we describe how this result fits in with other areas of research in complex contact geometry.