ON INVARIANT SUBMANIFOLDS OF ALMOST $\alpha$-COSYMPLECTIC $f$-MANIFOLDS

Abstract

In this paper, we investigate some properties of invariant submanifolds of almost $\alpha$-cosymplectic f- manifolds. We show that every invariant submanifold of an almost $\alpha$-cosymplectic f- manifold with Kaehlerian leaves is also an almost $\alpha$-cosymplectic f- manifold with Kaehlerian leaves. Moreover, we give a theorem on minimal invariant submanifold and obtain a necessary condition on a invariant submanifold to be totally geodesic. Finally, we study some properties of the curvature tensors of M and fM.

Keywords

• Almost -cosypmlectic f-manifold,invariant submanifold,semi parallel and 2-semi parallel submanifold

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