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

中文翻译：

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f-Kenmotsu 流形的不变子流形

在本文中，我们研究的不变子流形$F$-Kenmotsu 流形。首先，我们证明任何不变的子流形$F$-Kenmotsu 歧管又来了$F$-Kenmotsu 流形且最小。然后，我们给出完全测地线子流形的一些特征$F$-Kenmotsu 流形。我们研究 3 维子流形并证明 3 维子流形$F$-Kenmotsu 流形是完全测地线当且仅当它是不变的。还，$\eta$-Ricci 孤子被认为是不变的子流形$F$-Kenmotsu 流形。最后，构建了非平凡的例子来验证我们获得的一些结果。