  Within the general framework of spatially covariant theories of gravity, we
study the conditions for having only the two tensorial degrees of freedom.
Generally, there are three degrees of freedom propagating in the theory, of
which two are tensorial and one is of the scalar type. Through a detailed
Hamiltonian analysis, we find two necessary and sufficient conditions to evade
the scalar type degree of freedom. The first condition implies that the
lapse-extrinsic curvature sector must be degenerate. The second condition
ensures that the dimension of the phase space at each spacetime point is even,
so that the scalar type degree of freedom is eliminated completely. We also
compare our results with the previous studies, and apply our formalism to a
simple example, in which the Lagrangian is quadratic in the extrinsic
curvature.
