Construction of Real Space{Time from Complex Linear Metric Connections

Abstract

A construction of real space-time based on metric linear connections in a complex manifold is described. The construction works only in two or four dimensions. The four-dimensional case based on a connection reducible to group U(2, 2) can generate Riemann-Cartan geometry on the real submanifold of the original complex manifold. The possibility of connecting the appearance of Dirac fields with anholonomic complex frames is discussed.