Neutrino oscillations with three-generation mixings and mass hierarchy

We have analyzed the results of reactor and accelerator neutrino oscillation experiments in a model with mixing of three neutrino fields and a neutrino mass hierarchy. It is shown that $\nu_\mu \leftrightarrows \nu_e$ oscillations with $0.6 \le \Delta m^2 \le 100 \, \mathrm{eV}^2$ and amplitude larger than $2 \times 10^{-3}$ are not compatible with the existing limits on neutrino oscillations if the non-diagonal elements of the mixing matrix are small. Thus, if the excess of positron events recently observed in the LSND experiment is due to $\bar\nu_\mu \to \bar\nu_e$ oscillations, the mixing in the lepton sector is basically different from the CKM mixing of quarks.