curvature. The effects of the curvature term on the brane in linear approximation were studied in [@DGP; @CH], where it was shown that it leads to four-dimensional law of gravity on sufficiently small scales. The presence of this term also leads to qualitatively new features in cosmology, as demonstrated, in particular, in [@CHS; @SS]. For some recent reviews of the results connected with the induced-gravity term in the brane action, one may look into [@review].

Variation of action (\[act\]) gives us the equations describing the dynamics in the bulk $$\label{eq_mot1}
\mathcal{G}_{ab}+\Lambda_{\rm b}g_{ab}=0\, ,$$ and on the brane $$\label{eq_mot2}
m^2G_{ab}+\sigma h_{ab}=\tau_{ab}+M^3(K_{ab}-Kh_{ab})\, .$$ The second equation generalizes the Israel junction conditions [@Israel] and the corresponding equation of the Randall–Sundrum model to the presence of the scalar-curvature term on the brane ($m \ne 0$).

One can consider the Gauss identity $$\label{Gauss}
R_{abc}{}^d = h_a{}^f h_b{}^g h_c{}^k h^d{}_j {\cal R}_{fgk}{}^j + K_{ac}
K_b{}^d - K_{bc} K_a{}^d \, ,$$ and, following the original procedure of [@SMS], contract it once on the brane using equations (\[eq\_mot1\]) and (\[eq\_mot2\]). In this way, one obtains the effective equation on the brane that generalizes the result of [@SMS] to the presence of the brane curvature term: $$\label{effective}
G_{ab} + 