In the present paper, we define f -biminimal immersions. We consider f -biminimal curves in a Riemannian manifold and f -biminimal submanifolds of codimension 1 in a Riemannian manifold, and we give examples of fbiminimal surfaces. Finally, we consider f -biminimal Legendre curves in Sasakian space forms and give an example.

We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.