关键词: Riemannian product manifold, mixed geodesic submanifold, real space form and almost Riemannian product structure

Abstract:

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 submanifold of a Riemannian product manifold to be a locally symmetric and real space form.
 

Key words: Riemannian product manifold, mixed geodesic submanifold, real space form and almost Riemannian product structure