  It is well known that when a fermion propagates in curved space-time, its
spin couples to the curvature of background space-time. We propose that this
interaction for neutrinos propagating in early curved universe could give rise
to a new set of dispersion relations and then neutrino asymmetry at
equilibrium. We demonstrate this with the Bianchi models which describe the
homogeneous but anisotropic and axially symmetric universe. If the lepton
number violating processes freeze out at 10^{-37} second when temperature T ~
10^{15} GeV, neutrino asymmetry of the order of 10^{-10} can be generated. A
net baryon asymmetry of the same magnitude can thus be generated from this
lepton asymmetry either by a GUT B-L symmetry or by the electro-week sphaleron
processes which have B+L symmetry.
