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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)] {\it A. Bejancu} and {\it K. L. Duggal} introduced indefinite Sasakian structures $(f,\xi,\eta,g)$ and constructed a special example of index $s$ on $\bbfR^{2n+1}$. 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.

53C40Global submanifolds (differential geometry)
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)