In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If the...In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).展开更多
In this paper, applying the maximum pinciple due to Yau,We prove a curvature inequality and two sufficient conditions under which space-like hypersurfaces in the lorentzian manifolds are lotally umbilical.
文摘In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).
文摘In this paper, applying the maximum pinciple due to Yau,We prove a curvature inequality and two sufficient conditions under which space-like hypersurfaces in the lorentzian manifolds are lotally umbilical.
