Mimetic Horava Gravity and Surface terms

We consider mimetic Horava gravity, where the scalar field of mimetic gravity was used in the construction of diffeomorphism invariant models reducing to Horava gravity in the synchronous gauge. It will be shown that the gravitational action with the addition of the Gibbons-Hawking-York term and the mimetic Horava action are equivalent for manifolds whose topology is $R \times \Sigma$, where $\Sigma$ is a three-dimensional hypersurface; otherwise, the mimetic Horava action does not contain any surface terms.