# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 39 (2010) pp.351-387

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### Abstract

First we give the new elementary proof of the structure equations of $G_2$ and the congruence theorem of hypersurfaces of the purely imaginary octonions $\ImO$ under the action of $G_2$. Next, we classify almost complex structures of homogeneous hypersurfaces of $\ImO$ into 4-types.

MSC(Primary) 53C30 53C15 octonions, almost complex structure, $G_2$-congruent, $G_2$-orbits decomposition