  I discuss dynamical generation of neutrino masses in unconventional scenarios
where the background space-time geometry plays a crucial role. I discuss two
types of backgrounds: (i) Lorentz Violating and (ii) Geometries with Torsion.
In the former case, the violation of Lorentz symmetry, at a scale M, may be
viewed as a catalyst for mass generation and induced flavour oscillations among
neutrino species, which survive the limit of M taken to infinity, leading to a
hierarchy among neutrino masses. In the latter case, the (totally antisymmetric
components of the) torsion degrees of freedom correspond to a pseudoscalar
axion field in four space-time dimensions. This field is assumed to be mixed,
through non-diagonal kinetic terms, with ordinary axion fields that may exist
in the theory for other reasons and couple to neutrinos with chirality changing
Yukawa couplings. The torsion-ordinary-axion-field mixing is responsible,
through higher-loop anomalous graphs, for the dynamical generation of Majorana
masses. The latter scenarios can also be realised in some (compactified) string
theory models, where the (totally antisymmetric) torsion is played by the field
strength of the spin-one antisymmetric tensor (Kalb-Ramond) field, which exists
in the gravitational string multiplet.
