On quasi-Sasakian structure on a totally umbilical hypersurface of a six-dimensional Hermitian planar submanifold of Cayley algebra

Abstract

Six-dimensional planar submanifolds of Cayley algebra equipped with almost Hermitian structures induced by Brown — Gray three-fold vector cross products in are considered. We select the case when the almost Hermitian structures on such six-dimensional planar submanifolds of Cayley algebra are Hermitian, i. e. these structures are integrable. We study almost contact metric structures on totally umbilical hypersurfaces in such six-dimensional Hermitian pla­nar submanifolds of the octave algebra. We prove that if these almost contact metric structures on a totally umbilical hypersurface of a six-dimensional Hermitian planar submani­fold of Cayley algebra are quasi-Sasakian, then they are Sasakian.