International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 111-120

Oriented 6-dimensional submanifolds in the octonians, III

Hideya Hashimoto

Nippon Institute of Technology, Miyashiro, Saitaina 345, Japan

Received 11 May 1993; Revised 27 September 1993

Copyright © 1995 Hideya Hashimoto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.