THE STRUCTURE ON A SUBSPACE OF A SPACE WITH AN $f(3,-1)$-STRUCTURE

Jovanka Niki\'c

Abstract: Let $\Cal M^n$ be a manifold with an $f(3,-1)$-structure of rank $r$ and let $\Cal N^{n-1}$ be a hypersurface in $\Cal M^n$. The following theorem is proved: If the dimension of $T(\Cal V^{n-1}\cap f(T \Cal N^{n-1}))_p$ is constant, say $s$, for all $p\in \Cal N^{n-1}$, then $\Cal N^{n-1}$ 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 $\Cal M^n$ is integrable and if the transversal to $\Cal N^{n-1}$ can be found to lie in the distribution $M$.

Classification (MSC2000): 53C10, 53C15, 53C40, 51H20

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