Geometric interpretation of the curvature tensor in model space uni ed theory of gravitational and electromagnetic interactions

Abstract

The authors of [1] suggest that the space velocities of the particles are a four nonholonomic distribution on the manifold of higher dimensions. This distribution is given the 4-potential of the electromagnetic field. The equation of admissible (horizontal) geodesic for this distribution coincides with the equations of motion of a charged particle of the general theory of relativity. The metric tensor of the Lorentzian signature (+, -,-,-,) is defined on the distribution, which allows us to determine causality, as in the general theory of relativity. The authors introduced the covariant derivative (linear connection) and the curvature tensor for distribution. In [2], for any distribution of intrinsic connection, we construct its extension - extended connection. To ask for continuation connectivity means to identify some vector field on the corresponding distribution. Using a convenient coordinate system this field has the form: u = ∂_n + G_n^a ∂_n+a. The purpose of this paper is to find an explicit expression vector field u for which the curvature tensor of extended connectivity coincides with the tensor obtained in [1].