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 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. © 2012 Siraj Uddin et al.