A Riemannian space $V_n$ ($n=mr$), equipped with an integrable regular $H$-structure isomorphic to a hypercomplex algebra $h$ ($\dim h=r$), is considered as a real realization of a hypercomplex manifold ${\mathop V\limits^*}_m$ over the algebra $h$. The geometry of ${\mathop V\limits^*}_m$ can be mapped into the geometry of $V_n$. In particular, with the transformations of ${\mathop V\limits^*}_m$ are associated $H$-transformations (preserving the $H$-structure of the space) in $V_n$. The $H$-conformal and the $H$-projective transformations of $V_n$ are investigated.