In Minkowskian spaces, the helicity of a massless fermion is a conserv
ed quantity. In principle, this property may not hold when gravitation
al effects are not neglected. In this context, this work proves that t
he helicity of a massless neutrino is not conserved in curved spaces.
In order to show this fact, the time variation of the helicity in the
Heisenberg picture is calculated. Also, we verify that the differentia
l cross-section due to helicity flip of a massless neutrino in a curve
d space does not vanish as a result of the coupling between the spin a
nd the curvature of space-time.