  Theory of gravity is considered in the Regge-Teitelboim approach in which the
pseudo-Riemannian space is treated as a surface isometrically embedded in an
ambient Minkowski space of higher dimension. This approach is formulated in
terms of a field theory in which the original pseudo-Rimannian space is defined
by the field constant-value surfaces. The symmetry properties of the proposed
theory are investigated, and possible structure of the field-theoretical
Lagrangian is discussed.
