T violation without complex entries in lepton mixing matrix

We demonstrate that T invariance can be violated even when Pontecorvo--Maki--Nakagawa--Sakata lepton mixing matrix is real. We obtain a sufficient condition of T violation in neutrino oscillations in matter and electromagnetic field. In the two-flavor model we derive the T-violating spin-flavor transition probabilities. Then we prove that the transition probabilities for neutrino in moving medium in electromagnetic field differ from those for antineutrino in matter composed of antiparticles and electromagnetic field only in the sign of the T-violating term.