Fermion masses on a warped 6D world with the extra 2D sphere

In a warped 6-dimensional world with an extra 2-dimensional surface of a sphere, we find a 4-dimensional fermion mass formula with a zero mode. The warp factor is given by $\phi (\theta ,\varphi )=\sin{\theta }\cos{\varphi }$, which is a solution to the 6-dimensional Einstein equation with the bulk cosmological constant $\Lambda $ and the energy-momentum tensor of the bulk matter fields.