Abstract The object of the present paper is to introduce and investigate the P − curvature tensor that generalizes projective, conharmonic, M − projective and the set of W i curvature tensors introduced by Pokhariyal and Mishra. It is proven that pseudo-Riemannian manifolds admitting a traceless P -curvature tensor are Einstein and those admitting flat P -curvature tensor has a constant curvature. Classification theorems for pseudo-Riemannian manifolds admitting a divergence-free P -curvature tensor are given in each subspace of Gray’s decomposition of the covariant derivative of the Ricci tensor. Space–times having a flat P -curvature tensor or a divergence free P -curvature tensor are scrutinized. Finally, perfect fluid space–times admitting various features of the P -curvature tensor are considered.

中文翻译：

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关于广义投影P-曲率张量

摘要 本文的目的是介绍和研究P - 曲率张量，该张量概括了投影、共谐、M - 投影和由Pokhariyal 和Mishra 引入的W i 曲率张量的集合。证明了允许无迹P-曲率张量的伪黎曼流形是Einstein，而那些允许平坦的P-曲率张量的伪黎曼流形具有恒定曲率。在 Ricci 张量的协变导数的 Gray 分解的每个子空间中给出了准黎曼流形的分类定理，该定理允许无发散的 P 曲率张量。仔细检查具有平坦 P 曲率张量或无发散 P 曲率张量的时空。最后，考虑了允许 P 曲率张量的各种特征的完美流体时空。