Internal geometry of hypersurfaces in projectively metric space

In this paper, we study the internal geometry of a hypersurface V _n−1 embedded in a projectively metric space K _n , n ≥ 3, and equipped with fields of geometric-objects { G_nⁱ,G_i } \left\{ {G_n^i,{G_i}} \right\} and { H_nⁱ,G_i } \left\{ {H_n^i,{G_i}} \right\} in the sense of Norden and with a field of a geometric object { H_nⁱ,H_n } \left\{ {H_n^i,{H_n}} \right\} in the sense of Cartan. For example, we have proved that the projective-connection space P _n−1,n−1 induced by the equipment of the hypersurface V_{n - 1}   ì   K_n,  n 3 3 {V_{n - 1}} \subset {K_n},n \geq 3 , in the sense of Cartan with the field of a geometrical object { H_nⁱ,H_n } \left\{ {H_n^i,{H_n}} \right\} is flat if and only if its normalization by the field of the object { H_nⁱ,G_i } \left\{ {H_n^i,{G_i}} \right\} in the tangent bundle induces a Riemannian space R _n−1 of constant curvature K = −1/c.