Subtwistor Structures and Subtwistor Bundle

We introduce the notions of subtwistor structure and subtwistor bundle. Under consideration is some particular case of subtwistor structures, sub-Kahler structures. The subtwistor bundle for the four-dimensional sphere is described. We also provide some examples of the manifolds that admit or do not admit any subtwistor structure. For a real manifold of arbitrary dimension, we give conditions for the existence of a sub-Kaahler structure, which implies the existence of sub-Kaahler submanifolds.