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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.)