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The structure on a subspace of a space with an f(3,-1)-structure. (English) Zbl 0597.53031

Let \({\mathcal M}^ n\) be a manifold with an f(3,-1)-structure of rank r and let \({\mathcal N}^{n-1}\) be a hypersurface in \({\mathcal M}^ n\). The following theorem is proved: If the dimension of T(\({\mathcal N}^{n-1})\cap f(T{\mathcal N}^{n-1})_ p\) is constant, say s, for all \(p\in {\mathcal N}^{n-1}\), then \({\mathcal N}^{n-1}\) possesses a natural F(3,-1)- structure of rank s. It is also proved that the naturally induced F(3,- 1)-structure is integrable if the f(3,-1)-structure on \({\mathcal M}^ n\) is integrable and if the transversal to \({\mathcal N}^{n-1}\) can be found to lie in the distribution M.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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