  The Randall-Sundrum scenario with non-factorizable geometry and fifth
dimension y being an orbifold, is studied. It has two branes located at fixed
points of the orbifold. The four-dimensional metric is multiplied by a warp
factor exp[sigma(y)]. Recently, a new general expression for sigma(y) was
derived which has the orbifold symmetry y -> - y and explicitly reproduces
jumps of its derivative on both branes. It is symmetric with respect to the
branes. The function sigma(y) is determined by the Einstein-Hilbert's equations
up to a constant C. In the present paper we demonstrate that different values
of C result in quite different physical schemes. Three schemes are considered,
among which are: (i) the RS1 model; (ii) the RSSC model with a small curvature
of the five-dimensional space-time; (iii) the "symmetric" scheme with C=0. The
latter scenario is studied in detail.
