  A unified field theory for the description of matter in a curved space is
discussed. The description is based on a standard Lagrangianian formalism in a
pseudo-Euclidian 4D continuum using a 3-index tensor as independent variables.
The theory defines gravitational matter as a vector field and contains the
Einstein-Schwarzschild solution for the metric tensor in the case of stationary
spherical symmetry. Maxwell's equations, generalized for curved space, offer an
alternative to the expanding Universe explanation for the red shift phenomenon.
The theory contains a covariant law for conservation of matter and strictly
upports the Mach principle. A perturbation method allows a natural transition
to the special relativity, providing an explanation and the scale of elementary
particles parameters.
