On submanifolds of generalized recurrent manifolds

초록

In this paper we investigate some properties of submanifolds of generalized recurrent manifold (briefly, GRM<inf>n</inf>). Firstly, we show that a totally geodesic hypersurface of GRM<inf>n</inf> is a GRM<inf>n-1</inf>. Secondly, if GRM<inf>n</inf> is a Rie- mannian product manifold, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curva- Ture. Thirdly, a Riemannian product manifold of a space of constant curvature with itself is a GRMn. © 2015 Academic Publications, Ltd.

키워드