International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 111-120
doi:10.1155/S0161171295000159

Oriented 6-dimensional submanifolds in the octonions. 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.