Three flavor neutrino oscillation analysis of atmospheric neutrinos in Super-Kamiokande

We report on the results of a three-flavor oscillation analysis using Super-Kamiokande I atmospheric neutrino data, with the assumption of one mass scale dominance ($\Deltam_{12}^2$$=$0). No significant flux change due to matter effect, which occurs when neutrinos propagate inside the Earth for $\theta_{13}$$\neq$0, has been seen either in a multi-GeV $\nu_e$-rich sample or in a $\nu_\mu$-rich sample. A constraint on $\theta_{13}$ is given using Super-Kamiokande data only. Both normal and inverted mass hierarchy hypotheses are tested and both are consistent with observation.