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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.)
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