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Let $\psi:\M \to \SH$ be an isometric immersion of codimension 1, then thereexist symmetric $(1,1)$-tensors $S$ and $f$, a tangent vector field $U$ and asmooth function $\lambda$ on $\M$ that satisfy the compatibility equations of$\SH$. In this paper, we will deal with the converse problem: "Given aRiemannian manifold $\M$ with symmetric $(1,1)$-tensors $S$ and $f$, tangentvector field $U$ and smooth function $\lambda$ satisfying the conditionsmentioned above, can $\M$ then be isometrically immersed in $\SH$ in such a waythat $(g,S,f,U,\lambda)$ is realized as the induced structure?".

Hypersurfaces M^n in S^k x H^n-k+1