The scalar sector of the Randall--Sundrum model is discussed. The effective potential for the Standard Model Higgs-boson (h) interacting with Kaluza--Klein excitations of the graviton (h_\mu^{\nu  n}) and the radion (\phi ) has been derived and it has been shown that  only the Standard Model vacuum solution of \partial V/\partial h =0 is allowed. The theoretical and experimental consequences of the curvature-scalar mixing \xi R \hat H^\dagger \hat H introduced on the visible brane are considered and simple sum rules that relate the couplings of the mass eigenstates h and \phi to pairs of vector bosons and fermions are derived. The sum rule for the ZZh and ZZ\phi couplings in combination with LEP/LEP2 data implies that not both the h and \phi can be light. We present explicit results for the still allowed region in the (m_h,{m_\phi }) plane that remains after imposing the LEP upper limits for non-standard scalar couplings to a ZZ pair. The phenomenological consequences of the mixing are investigated and, in particular, it is shown that the Higgs-boson decay h \to \phi \phi would provide an experimental signature for non-zero \xi and can have a very substantial impact on the Higgs-boson searches, having {BR}(h \to \phi \phi ) as large as 30 \div 40%.

PACS numbers: 04.50.+h, 12.60.Fr