Abstract
We present two new solutions to Einstein's equations in (1+5)-spacetime with positive bulk cosmological constant. For these solutions, it is shown that the zero modes of all local fields are localized at different points on the brane in the extra space only through the gravitational interaction. We also suggest a pure gravitational mechanism explaining the origin of three generations of the Standard Model fermions and explicitly show that localized fermions are stuck at different points on the brane in the extra space.