The geometrical structure of a complexified theory of gravitation

Outlines the procedure for the complexification of the tangent bundle over a four-dimensional space-time manifold. By introducing a connection and metric compatible with the complex structure, the authors form the geometrical basis for a new (complexified) theory of gravitation whose fundamental gauge group is U(3,1). They further prove that the Lagrangian for the theory is necessarily real when the connection is compatible with the metric.