THE $(\psi,\xi,\eta,\overline g)$ SUBSPACES OF THE SPACE WITH THE $\varphi(4,-2)$ STRUCTURE

Jovanka Niki\'c

Abstract: Let a tensor field $\varphi$, $\varphi\not=0$, $\varphi\not=1$, of type (1,1) and of class $C^\infty$ be given on $M^n$ such that $\varphi^4-\varphi^2=0$, and rank\,$\varphi=n-1$. The structure $\Phi=2\varphi-1$ is an almost product structure. $\Phi$ induces on hypersurface $K$ a Sato structure. In this paper it is proved that the structure Sato $\psi$ induced by $\Phi$ on $K^*$ is equal to the $\overline\varphi$. ($\overline\varphi$ is the restriction of the structure $\varphi$ on $K^*$).

Keywords: Almost product structure, structure Sato, hypersurface, restriction of the structure, almost paracontact Riemannian structure

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

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