The (psi,xi,eta,g) Subspaces of the Space with the Phi(4,-2) Structure

Jovanka Nikić

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 $K^*$).