The gravitational Lagrangian can be written as a summation of a bulk and a
total derivative term. For some theories of gravity such as Einstein gravity,
or more general Lovelock gravities, there are Lagrangian holographic relations
between the bulk and the total derivative term such that the latter is fully
determined by the former. However at the $D\rightarrow 2\&4$ limit, the bulks
of Einstein or Gauss-Bonnet theories become themselves total derivatives.
Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities
gives rise to some two-dimensional or four-dimensional scalar-tensor theories
respectively. We obtain the holographic relations for the $D = 2$ and $D = 4$
cases, which have the same form as the holographic relations in pure gravity in
the foliation independent formalism.
