  Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat
background metric, we obtain the effective 4D equation for massive neutrino in
a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D
Ricci-flat metric. We use the fact that the spin connection is defined to an
accuracy of a vector, so that the covariant derivative of the spinor field is
strongly dependent of the background geometry. We show that the mass of the
neutrino can be induced from the extra space-like dimension.
