  The phenomenon of neutrino oscillations is studied usually as a mixing
between the flavor neutrinos and the neutrinos having a definite mass. The
mixing angles and the mass eigenvalues are treated independently in order to
accommodate the experimental data. We suggest that neutrino oscillations are
connected to the structure of spacetime. We expand on a recently proposed
model, where two "mirror" branes coexist. One brane hosts left-handed particles
(our brane), while the other brane hosts right-handed particles. Majorana-type
couplings mixes neutrinos in an individual brane, while Dirac-type couplings
mixes neutrinos across the brares. We first focus our attention in a single
brane. The mass matrix, determined by the Majorana mass, leads to mass
eigenstates and further to mixing angles identical to the mixing angles
proposed by the tri-bimaximal mixing. When we include the Dirac-type coupling,
connecting the two branes, we obtain a definite prediction for the transition
to a sterile neutrino (right-handed neutrino). With m_L (m_R) the Majorana mass
for the left (right) brane, we are able to explain the solar and the
atmospheric neutrino data with m_L = 2m_R and m_R = 10**(-2) eV.
