Nonlinear connections for curved twistor spaces

Abstract

A holomorphic connection on (1, 0)-vector fields which is intrinsically defined on any curved twistor space is described. Although it is a local operator, it is given in terms of the nonlocal geometry of the twistor space corresponding to the local geometry of the spacetime. The connection is represented in local coordinates by a system ofnonlinear first-order partial differential operators. It has torsion but no curvature. A parallelism is given explicitly, and an example is computed.