  We study embedding gravity, a modified theory of gravity, in which our
space-time is assumed to be a four-dimensional surface in flat ten-dimensional
space. Based on a simple geometric idea, this theory can be reformulated as
General Relativity with additional degrees of freedom and contribution to
action, which can be interpreted as describing dark matter. We study the
canonical formalism for such a formulation of embedding gravity. After solving
simple constraints, the Hamiltonian is reduced to a linear combination of four
first class constraints with Lagrange multipliers. There still remain six pairs
of second class constraints. Possible ways of taking these constraints into
account are discussed. We show that one way of solving the constraints leads to
the canonical system going into the previously known canonical formulation of
the complete embedding theory with an implicitly defined constraint.
