In this paper, we define a (1, 3)-tensor field T(X, Y)Z on Kenmotsu manifolds and give a necessary and sufficient condition for T to be a curvature-like tensor. Next, we present some properties related to the curvature-like tensor T and prove that \(M^{2m+1}\) is an \(\eta \)-Einstein–Kenmotsu manifold if and only if \(\sum ^{m}_{j=1}T( \varphi (e_j), e_j) X = 0\). Besides, we define a (1, 4)-tensor field t on the Kenmotsu manifold M which determines when M is a Chaki T-pseudo-symmetric manifold. Then, we obtain a formula for the covariant derivative of the curvature tensor of Kenmotsu manifold M. We also find some conditions under which an \(\eta \)-Einstein–Kenmotsu manifold is a Chaki T-pseudo-symmetric. Finally, we give an example to verify our results and prove that every three-dimensional Kenmotsu manifold is a generalized pseudo-symmetric manifold.

在本文中，我们在Kenmotsu流形上定义了（1，3）张量场T（X，  Y）Z，并给出了使T成为曲率张量的充要条件。接下来，我们介绍一些与曲率张量T相关的性质，并证明\（M ^ {2m + 1} \）是\（\ eta \）- Einstein–Kenmotsu流形，当且仅当\（\ sum ^ {m} _ {j = 1} T（\ varphi（e_j），e_j）X = 0 \）。此外，我们在Kenmotsu流形M上定义了（1，4）张量场t，它确定M何时是Chaki T-伪对称流形。然后，我们获得了Kenmotsu流形M曲率张量的协变量导数的公式。我们还找到了一些条件，其中\（\ eta \）- Einstein–Kenmotsu流形是Chaki T-伪对称。最后，我们给出一个例子来验证我们的结果，并证明每个三维Kenmotsu流形都是广义的伪对称流形。