Mu-tau neutrino refraction and collective three-flavor transformations in supernovae

We study three-flavor collective neutrino transformations in the dense-neutrino region above the neutrino sphere of a supernova core. We find that two-flavor conversions driven by the atmospheric mass difference and the 13-mixing angle capture the full effect if one neglects the second-order difference between the nu(m) and nu(tau) refractive index. Including this mu- tau matter term'' provides a resonance at a density of rho approximate to 3 X 10(7) g cm(-3) that typically causes significant modifications of the overall nu(e) and (nu) over bar (e) survival probabilities. This effect is surprisingly sensitive to deviations from maximal 23- mixing, being different for each octant.