In this paper we study a Riemann--Otsukl space $R-O_n$ and one of its $m$-dimensional $(m<n)$ subspaces, which is also a Riemann--Otsuki space, (see [1] and [2]). We denote that subspace by $R-O_m$. Our aim is to determine the conditions by which the autoparallel curves of $R-O_m$ are the autoparallel curves of $R-O_n$, too.