Orthogonal almost complex structures of oriented 6-dimensional submanifolds in the octonions and hypersurfaces in the purely imaginary octonions

This paper is a survey of the orthogonal almost complex structures on oriented 6-dimensional submanifolds the octonions C. First we give a classification of 6-dimensional extrinsic homogeneous almost Hermitian submanifolds of C. Next, we classify almost complex structures of homogeneous hypersurfaces of purely imaginary octonions ImC into 4 types.