Twistors and nearly autoparallel maps

The purpose of the present paper is to investigate the problem of definition of twistors on generic curved spaces. Firstly, we consider nearly geodesic (autoparallel) maps of (pseudo)-Riemannian spaces. Secondly, we shall define nearly autoparallel twistor equations which are compatible on nearly conformally flat spaces. Finally, we shall study nearly auto-parallel twistor structures generating curved spaces and vacuum Einstein spaces.