Solar-neutrino oscillations and third-flavour admixture

With one \Delta m^2 of the appropriate order of magnitude to solve the atmospheric neutrino problem, we study the resulting three-generation vacuum-oscillation fit to the solar neutrino flux. An explanation of the atmospheric neutrino composition in terms of pure \nu_\mu \to \nu_\tau oscillations is easily compatible with the well-known two-flavour oscillation solution for solar neutrinos. The allowed parameter region in the \sin^2(2\theta_{12})--\Delta m^2 plane changes little with increasing values of the mixing element U_{e3}, provided this is less than about 0.4. We find that the threefold maximal mixing is disfavoured.