Sasakian hypersurfaces of six-dimensional Hermitian manifolds of the Cayley algebra. (English. Russian original) Zbl 1079.53103
Sb. Math. 194, No. 8, 1125-1136 (2003); translation from Mat. Sb. 194, No. 8, 13-24 (2003).
The paper under review is devoted to Sasakian hypersurfaces in 6-dimensional submanifolds of the Cayley algebra. It continues the studies of the author concerning almost contact metric structures on hypersurfaces in 6-dimensional submanifolds of the octave algebra. The results of the paper are next briefly stated. A criterion for the minimality of a Sasakian hypersurface in a 6-dimensional Hermitian sub-manifold of the octave algebra is obtained. It is proved that the type number of a Sasakian hypersurface in a 6-dimensional Hermitian submanifold of the octave algebra is four or five. It is also proved that a Sasakian hypersurface in a 6-dimensional Hermitian submanifold of the Cayley algebra is minimal if and only if it is ruled.
Reviewer: Adrian Sandovici (Groningen)
MSC:
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C40 | Global submanifolds |
| 17A35 | Nonassociative division algebras |
