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On minimality of a Sasakian hypersurface in a $$W_ 3$$-manifold. (English) Zbl 1052.53045
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 $$M^{2n}$$.

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