Dual Riemannian spaces of constant curvature on a normalized hypersurface

In this paper, the following results are obtained: 1) It is proved that, in the fourth order differential neighborhood, a regular hypersurface V _n−1 embedded into a projective-metric space K _n , n ≥ 3, intrinsically induces a dual projective-metric space $ \bar K_n $ \bar K_n . 2) An invariant analytical condition is established under which a normalization of a hypersurface V _n−1 ⊂ K _n (a tangential hypersurface $ \bar V_{n - 1} $ \bar V_{n - 1} ⊂ $ \bar K_n $ \bar K_n ) by quasitensor fields H _n ⁱ , H _i ($ \bar H_n^i $ \bar H_n^i , $ \bar H_i $ \bar H_i ) induces a Riemannian space of constant curvature. If the two conditions are fulfilled simultaneously, the spaces R _n−1 and $ \bar R_{n - 1} $ \bar R_{n - 1} are spaces of the same constant curvature $ K = - \tfrac{1} {c} $ K = - \tfrac{1} {c} . 3) Geometric interpretations of the obtained analytical conditions are given.