A Note on Invariant Submanifolds of CR-Integrable Almost Kenmotsu Manifolds

Abstract

The present paper deals with invariant submanifolds of $CR$-integrable almost Kenmotsu manifolds. Among others it is proved that every invariant submanifold of a $CR$-integrable $(k,\mu)'$-almost Kenmotsu manifold is totally geodesic. By a counter example we have shown that the converse is not true, in general. Finally, we construct an example of an invariant submanifold of a $CR$-integrable $(k,\mu)'$-almost Kenmotsu manifold which is totally geodesic.