  The gauge symmetry inherent in the concept of manifold has been discussed.
Within the scope of this symmetry the linear connection or displacement field
can be considered as a natural gauge field on the manifold. The gauge invariant
equations for the displacement field have been derived. It has been shown that
the energy-momentum tensor of this field conserves and hence the displacement
field can be treated as one that transports energy and gravitates. To show the
existence of the solutions of the field equations we have derived the general
form of the displacement field in Minkowski space-time which is invariant under
rotation and space and time inversion. With this anzats we found
spherically-symmetric solutions of the equations in question.
