  The dynamics of fermions on curved spacetime requires a spin connection,
which contains a part called contorsion, an auxiliary field without dynamics
but fully expressible in terms of the axial current density of fermions. Its
effect is the appearance of a quartic interaction of all fermions in the
action, leading to a nonlinear Dirac equation involving all fermions present.
Noting that left and right-chiral fermions may couple to contorsion by
different strengths, we show that all fermions gain an effective mass when
propagating through fermionic matter. This may have an observable effect on
neutrino oscillations. In particular we find that different neutrino flavors
can mix even if they have zero rest mass in vacuum, without requiring fields
beyond the Standard Model.
