TWISTORS AND G-STRUCTURES

The authors distinguish a class of twistor spaces Z = P X (G)S that are associated, following Berard-Bergery and Ochiai, with G-structures P on even-dimensional manifolds and connections in P. It is assumed that S = G/H is a complex totally geodesic submanifold of the affine symmetric space GL2n(R)/GL(n)(C) . This class includes all the basic examples of twistor spaces fibered over an even-dimensional base. The integrability of the canonical almost complex structure J(Z) and the holomorphy of the canonical distribution H(Z) in Z are studied in terms of some natural H-structure with a connection on the manifold Z. Some examples are also treated.