Twistor bundles of foliated Riemannian manifolds (Q6616245)

This is an overview of the theory of twistors on foliated manifolds, which has been developed in papers by several authors.\N\NThe authors explain the construction of the twistor space of the normal bundle of a foliation and demonstrate that the classical constructions of twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic maps. Since any orbifold can be understood as the leaf space of a suitably defined Riemannian foliation, orbifold versions of the classical results can be (and are) understood as simple consequences of the results on foliated maps. Finally, the suspension construction is recalled; this can be (and is) used to construct examples of transversely harmonic maps between foliated manifolds and to discuss the twistor methods in this case.\N\NFor the entire collection see [Zbl 1532.53004].