TWISTORS AND -STRUCTURES

The authors distinguish a class of twistor spaces that are associated, following Bérard-Bergery and Ochiai, with -structures on even-dimensional manifolds and connections in . It is assumed that is a complex totally geodesic submanifold of the affine symmetric space . This class includes all the basic examples of twistor spaces fibered over an even-dimensional base. The integrability of the canonical almost complex structure and the holomorphy of the canonical distribution in are studied in terms of some natural -structure with a connection on the manifold . Some examples are also treated.