  Three-generation MSW effect in curved spacetime is studied and a brief
discussion on the gravitational correction to the neutrino self-energy is
given. The modified mixing parameters and corresponding conversion
probabilities of neutrinos after traveling through celestial objects of
constant densities are obtained. The method to distinguish between the normal
hierarchy and inverted hierarchy is discussed in this framework. Due to the
gravitational redshift of energy, in some extreme situations, the resonance
energy of neutrinos might be shifted noticeably and the gravitational effect on
the self-energy of neutrino becomes significant at the vicinities of spacetime
singularities.
