We study properties of invariant submanifolds of  <i>K</i>-manifolds as well as of some special types of 
<i>K</i>-manifolds. Moreover, we investigate  properties of submersions between 
<i>f</i>-manifolds. In particular, we find some curvature identities when the total space is an <i>S</i>-manifold and the base space is K&auml;hler.