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On the existence of degenerate hypersurfaces in Sasakian manifolds. (English) Zbl 0977.53056
In [Int. J. Math. Math. Sci. 16, 545-556 (1993; Zbl 0787.53048)] A. Bejancu and K. L. Duggal introduced indefinite Sasakian structures \((f,\xi,\eta,g)\) and constructed a special example of index \(s\) on \(\mathbb{R}^{2n+1}\). In the paper under review the author is concerned with hypersurfaces \(M\) of the latter space, which are tangent to the structure vector field \(\xi\). He shows: If \(s=n\) then \(M\) always is non-degenerate, but for \(s=1\) degenerate examples exist.

MSC:
53C40 Global submanifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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