Holographic relationships in Lovelock type brane gravity

We show that the Lovelock type brane gravity is naturally holographic by providing a correspondence between bulk and surface terms that appear in the Lovelock-type brane gravity action functional. We prove the existence of relationships between the ${\mathcal{L}}_{bulk}$ and ${\mathcal{L}}_{surf}$ allowing ${\mathcal{L}}_{surf}$ to be determined completely by ${\mathcal{L}}_{bulk}$. In the same spirit, we provide relationships among the various conserved tensors that this theory possesses. We further comment briefly on the correspondence between geometric degrees of freedom in both bulk and surface space.