We study three-dimensional trans-Sasakian manifolds admitting η -Ricci solitons. Actually, we investigate manifolds whose Ricci tensor satisfy some special conditions, such as cyclic parallelity, Ricci semisymmetry, and 𝜙 -Ricci semisymmetry, after reviewing the properties of the second-order parallel tensors on these manifolds. We determine the form of the Riemann curvature tensor for trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces. We also present some classification results for trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces.

中文翻译：

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承认η-Ricci孤子和Trans-Sasakian流形作为Kagan子射影空间的三维Trans-Sasakian流形的一些表征

我们研究了承认 η -Ricci 孤子的三维跨萨萨基流形。实际上，在回顾了这些流形上的二阶平行张量的性质之后，我们研究了 Ricci 张量满足一些特殊条件的流形，例如循环平行性、Ricci 半对称性和 𝜙 -Ricci 半对称性。我们将维数大于 3 的跨 Sasakian 流形的黎曼曲率张量的形式确定为 Kagan 亚射影空间。我们还提供了一些维度大于 3 的跨 Sasakian 流形作为 Kagan 子投影空间的分类结果。