  A generalized definition of a frame of reference in spaces with affine
connections and metrics is proposed based on the set of the following
differential-geometric objects:
  (a) a non-null (non-isotropic) vector field,
  (b) the orthogonal to the vector field sub space,
  (c) an affine connection and the related to it covariant differential
operator determining a transport along the given non-null vector filed.
  On the grounds of this definition other definitions related to the notions of
accelerated, inertial, proper accelerated and proper inertial frames of
reference are introduced and applied to some mathematical models for the
space-time. The auto-parallel equation is obtained as an Euler-Lagrange's
equation. Einstein's theory of gravitation appears as a theory for
determination of a special frame of reference (with the gravitational force as
inertial force) by means of the metrics and the characteristics of a material
distribution.
  PACS numbers: 0490, 0450, 1210G, 0240V
