Invariant submanifolds of f-Kenmotsu manifolds

Abstract

In the present paper, we study the invariant submanifolds of [Formula: see text]-Kenmotsu manifolds. Firstly, we show that any invariant submanifold of [Formula: see text]-Kenmotsu manifold is again [Formula: see text]-Kenmotsu manifold and minimal. Then, we give some characterizations of totally geodesic submanifolds of [Formula: see text]-Kenmotsu manifolds. We study 3-dimensional submanifold and prove that a 3-dimensional submanifold of [Formula: see text]-Kenmotsu manifold is totally geodesic if and only if it is invariant. Also, [Formula: see text]-Ricci soliton is considered on invariant submanifold of [Formula: see text]-Kenmotsu manifolds. Lastly, the non-trivial examples are constructed to verify some of our obtained results.