  We propose a four-neutrino model which can reconcile the existing data coming
from underground experiments in terms of neutrino oscillations, together with
the hint from the LSND experiment and a possible neutrino contribution to the
hot dark matter of the Universe. It applies the idea that extra compact
dimensions, probed only by gravity and possibly gauge-singlet fields, can lower
the fundamental scales such as the Planck, string or unification scales. Our
fourth light neutrino $\nu_s$ ($s$ for sterile) is identified with the zero
mode of the Kaluza-Klein states. To first approximation \nu_sterile combines
with the nu_mu in order to form a Dirac neutrino with mass in the eV range
leaving the other two neutrinos massless. The smallness of this mass scale
(suitable for LSND and Hot Dark Matter) arises without appealing neither to a
see-saw mechanism nor to a radiative mechanism, but from the volume factor
associated with the canonical normalization of the wave-function of the bulk
field in the compactified dimensions. % On the other hand the splitting between
\nm and \nu_sterile (atmospheric scale) as well as the mass of the two other
neutrinos (solar mass scale) arise from the violation of the fermion number on
distant branes. We also discuss alternative scenarios involving
flavour-changing interactions. In one of them \ne can be in the electron-volt
range and therefore be probed in beta decay studies.
