ACTA MATHEMATICA SCIENTIA, cilt.24, sa.4, ss.549-558, 2004 (SCI-Expanded)
In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant sub-manifold of a Riemannian product manifold to be a locally symmetric and real space form.