Hermitian geometry of six-dimensional symmetric submanifolds of Cayley algebra
The author studies the 6-dimensional submanifolds \(M^6\) of the Cayley algebra \(\mathbb{O}\) on which an almost Hermitian structure is canonically induced. He calls \(M^6\) a Hermitian submanifold if it admits a non-Kählerian but integrable (i.e., Hermitian) structure. The class of Ricci-type submanifolds is introduced which includes the class of submanifolds on which a Kählerian structure is induced. Generalizing the results in [\textit{M. B. Banaru} and \textit{V. F. Kirichenko}, Russ. Math. Surv. 49, 223-224 (1994; Zbl 0855.53027)], he gives a complete classification of the Ricci-type Hermitian locally symmetric submanifolds \(M^6 \subset {\mathbb{O}}\).
scientific article; zbMATH DE number 1028420