Current issue

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

DOI

10.5922/0321-4796-2022-53-1

Pages

5-12

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.

Reference

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