  We consider the approach to gravity in which four-dimensional curved
spacetime is represented by a surface in a flat Minkowski space of higher
dimension. After a short overview of the ideas and results of such an approach
we concentrate on the study of the so-called splitting gravity, a form of this
description in which constant value surface of a set of scalar fields in the
ambient flat space-time defines the embedded surface. We construct a form of
action which is invariant w.r.t. all symmetries of this theory. We construct
the canonical formalism for splitting gravity. The resulting theory turns out
to be free of constraints. However, the Hamiltonian of this theory is an
implicit function of canonical variables. Finally, we discuss the path integral
quantization of such a theory.
