HASHIMOT Hideya, OHASHI Misa,
Orthogonal almost complex structures of hypersurfaces of purely imaginary octonions.
Hokkaido Mathematical Journal, 39 (2010) pp.351-387
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.
|Uncontrolled Keywords||octonions, almost complex structure, $G_2$-congruent, $G_2$-orbits decomposition|