We suggest model equations, which, from some point of view, describe localinteraction of three physical fields: a field of matter, an electromagneticfield and a gravitational field. A base of the model is a field of matterdescribed by the wave function of fermion satisfying the equation similar toDirac equation for electron. Electromagnetic and gravitational fields appear asthe gauge fields for this equation. We have found the connection between thesefields and the curvature tensor of Riemannian manifold. We present a mainLagrangian from which the equations of the model are deduced. The covariance ofthe model equations under changes of coordinates is considered. We developmathematical techniques needed for the model connected with an exterior algebraof Euclidean or Riemannian space. The exterior algebra is considered as abialgebra with two operations of multiplications -- an exterior multiplicationand Clifford multiplication. We define a structure of Euclidean or Riemannianspace on the exterior algebra, which leads to the notions of Spin-isometricchange of coordinates and Spin-isometric manifold used in the model.In therevised paper we correct an error with the formula $G_{ij}=-U^{-1}D_{ij}U/2$,(now U=1).
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