Pure Geometric Branes and Mass Hierarchy

We consider a toy model with flat thin branes embedded in a 5-dimensional Weyl integrable manifold, where the geometric Weyl scalar provides the material that constitute the brane configurations. The brane configuration is similar to the Randall-Sundrum model. However, it is found that the massless graviton is localized on the brane with negative tension. So in order to solve the gauge hierarchy problem our world should be confined on the positive tension brane, and this is crucial to reproduce a correct Friedmann-like equation on the brane. The spacings of graviton mass spectrum are very tiny, but these massive gravitons are hidden in low energy experiments because they are weakly coupled with matter on the brane.