A Classification of a Totally Umbilical Slant Submanifold of Cosymplectic Manifolds

Abstract

We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold $M$ of a cosymplectic manifold $\bar{M}$ is either an anti-invariant submanifold or a 1−dimensional submanifold. We show that every totally umbilical proper slant submanifold of a cosymplectic manifold is totally geodesic.