Transformations in hypercomplex Riemannian spaces

It is well known that an integrable regular $H$-structure induces on a real manifold $M_n$ the structure of a hypercomplex analytic manifold ($h$-manifold) $\mathop M\limits^*{}_m$. We prove that the Lie derivative of a pure tensor $T$ on $M_n$ is an $h$-derivative of Lie providing $T$ is $h$-analytic. With the $h$-derivative of Lie there is associated on $\mathop M\limits^*{}_m$ the hypercomplex derivative of Lie. This enables us to associate to the motions and affine collineations in the Riemannian space $\mathop V\limits^*{}_m$ corresponding transformations in a real space $V_n$.