  In the first part of this work we review the equations of motion for the
brane presented in Friedmann-Robertson-Walker (FRW) form, when bulk is
five-dimensional (A)dS Black Hole. The spacelike (timelike) FRW brane equations
are considered from the point of view of their representation in the form
similar to two-dimensional CFT entropy, so-called Cardy-Verlinde (CV) formula.
The following five-dimensional gravities are reviewed: Einstein,
Einstein-Maxwell and Einstein with brane quantum corrections. The second part
of the work is devoted to study FRW brane equations and their representation in
CV form, brane induced matter and brane cosmology in Einstein-Gauss-Bonnet (GB)
gravity. In particular, we focus on the inflationary brane cosmology. The
energy conditions for brane matter are also analyzed. We show that for some
values of GB coupling constant (bulk is AdS BH) the brane matter is not CFT.
Its energy density and pressure are not always positive.
