[en] We present an extension of the singlet majoron gauge model which realizes a novel scheme of geometrical neutrino mass hierarchy proposed recently by Glashow, wherein ν_e and ν_μ are Majorana particles with m_νe∼m_νμ∼10^-3 eV while ν_τ is a Dirac particle with a mass of 17 keV. Our model explains the solar-neutrino deficit via the Mikheyev-Smirnov-Wolfenstein mechanism and accounts for the recently reported anomaly in beta-decay spectra in a natural manner without any undesirable fine tuning of parameters. An interesting consequence of the model is that ν_τ is short lived with a lifetime of ∼10^-3--10^-1 sec