  We study decoherence effects in neutrino flavour oscillations in curved
spacetime with particular emphasis on the lensing in a Schwarzschild geometry.
Assuming Gaussian wave packets for neutrinos, we argue that the decoherence
length derived from the exponential suppression of the flavour transition
amplitude depends on the proper time of the geodesic connecting the events of
the production and detection in general gravitational setting. In the weak
gravity limit, the proper time between two events of given proper distance is
smaller than that in the flat spacetime. Therefore, in presence of a
Schwarzschild object, the neutrino wave packets have to travel relatively more
physical distance in space to lapse the same amount of proper time before they
decoher. For non-radial propagation applicable to the lensing phenomena, we
show that the decoherence, in general, is sensitive to the absolute values of
neutrino masses as well as the classical trajectories taken by neutrinos
between the source and detector along with the spatial widths of neutrino wave
packets. At distances beyond the decoherence length, the probability of
neutrino flavour transition due to lensing attains a value which depends only
on the leptonic mixing parameters. Hence, the observability of neutrino lensing
significantly depends on these parameters and in-turn the lensing can provide
useful information about them.
