In this paper there are discussed the three-component distributions of affine space $A_{n+1}$. Functions $\left\{{ℳ}^{\sigma }\right\}$, which are introduced in the neighborhood of the second order, determine the normal of the first kind of $\mathscr{H}$-distribution in every center of $\mathscr{H}$-distribution. There are discussed too normals $\left\{{𝒵}^{\sigma }\right\}$ and quasi-tensor of the second order $\left\{{𝒮}^{\sigma }\right\}$. In the same way bunches of the projective normals of the first kind of the $ℳ$-distributions were determined in the differential neighborhood of the second and third order.

In this paper we define generalized Kählerian spaces of the first kind $\left(G{\underset{1}{K}}_N\right)$ given by (2.1)–(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ($G{\underset{1}{K}}_N$ and $G{\underset{1}{\overline{K}}}_N$) and for them we find invariant geometric objects.