The object of the paper is to study the compatibility of φ(Ric)-vector fields on almost pseudo-Ricci symmetric manifolds, briefly A(PRS)n. First, we show the existence of an A(PRS)n whose basic vector field w(X) is a φ(Ric)-vector field by constructing a non-trivial example. Then, we investigate the properties of the Riemann and Weyl compatibility of A(PRS)n under certain conditions. We consider an A(PRS)4 space-time whose basic vector fields π(X) and ω(X) is φ(Ric)-vector fields of constant length. Moreover, we show that an A(PRS)4 space-time whose Ricci tensor is of Codazzi type and basic vector field ω(X) is φ(Ric)-vector field is purely electric space-time.

中文翻译：

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几乎伪 Ricci 对称流形上 φ(Ric)-向量场的兼容性

本文的目的是研究兼容性φ(里克)- 几乎伪 Ricci 对称流形上的向量场，简要介绍一种(个人退休计划)n. 首先，我们证明存在一个一种(个人退休计划)n其基本向量场w(X)是一个φ(里克)-vector 场通过构造一个非平凡的例子。然后，我们研究了 Riemann 和 Weyl 相容性的性质一种(个人退休计划)n在一定条件下。我们考虑一个一种(个人退休计划)4其基本向量场的时空π(X)和ω(X)是φ(里克)- 恒定长度的向量场。此外，我们证明了一个一种(个人退休计划)4Ricci 张量为 Codazzi 型和基本向量场的时空ω(X)是φ(里克)-矢量场是纯电时空。