The object of the present paper was to study biharmonic maps on f-Kenmotsu manifolds and with Schouten–van Kampen connection. With help this connection, our results provided important insights related harmonic maps.

In the present paper, we prove that if metric of a three dimensional almost Kenmotsu manifold with $\textbf{Q}\phi=\phi \textbf{Q}$ whose scalar curvature remains invariant under chracterstic vector field $\zeta$, admits non-trivial Yamabe solitons, then is constant sectional or Ricci simple.

In the present paper we obtained 2 identities, which are satisfied by Riemann curvature tensor of generalized Kenmotsu manifolds. There was an analytic expression for third structure or f -holomorphic sectional GK -manifold. We separated classes manifolds and collected their local characterization.

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.