On minimality of a Sasakian hypersurface in a \(W_ 3\)-manifold. (English) Zbl 1052.53045

Banaru, M.

Saitama Math. J. 20, 1-7 (2002).

The main theorem of the paper is: Let \(N\) be a Sasakian hypersurface in a special Hermitian manifold \(M^{2n}\) and let \(\sigma\) be the second fundamental form of the immersion of \(N\) into \(M^{2n}\). Then \(N\) is a minimal submanifold of \(M^{2n}\) if and only if \(\sigma\left(\xi,\xi\right) =0\), with \(\xi\) being the vector field defining the almost contact metric structure on \(N\) induced by the almost Hermitian structure on \(M^{2n}\).

Reviewer: Andrzej Piatkowski (Łódź)

MSC:

53C40	Global submanifolds
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords:

almost contact metric structure; Sasakian manifold; special Hermitian manifold