Oriented 6-dimensional submanifolds in the octonians, III

Abstract

In this paper, we classify 6-dimensional almost Hermitian submanifolds in the octonians 𝕆 according to the classification introduced by A. Gray and L. Hervella. We give new examples of quasi-Käthler and ∗-Einstein submanifolds in 𝕆. Also, we prove that a 6-dimensional weakly ∗-Einstein Hermitian submanifold in 𝕆 is totally geodesic.

Keywords

• octonians
• 6-dimensional almost Hermitian submanifolds.