Abstract The objective, in this paper, is to obtain the curvature properties of ( t − z ) -type plane wave metric studied by Bondi et al. 1959. For this a general ( t − z ) -type wave metric is considered and the condition for which it obeys Einstein’s empty spacetime field equations is obtained. It is found that the rank of the Ricci tensor of ( t − z ) -type plane wave metric is 1 and is of Codazzi type. Also it is proved that it is not recurrent but Ricci recurrent, conformally recurrent and hyper generalized recurrent. Moreover, it is semisymmetric and satisfies the Ricci generalized pseudosymmetric type condition P ⋅ P = − 1 3 Q ( R i c , P ) . It is interesting to note that, physically, the energy momentum tensor describes a radiation field with parallel rays and geometrically it is a Codazzi tensor and semisymmetric. As special case, the geometric structures of Taub’s plane symmetric spacetime metric are deduced. Comparisons between ( t − z ) -type plane wave metric and pp-wave metric with respect to their geometric structures are viewed.

中文翻译：

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(t−z) 型平面波度量的曲率特性

摘要 本文的目的是获得 Bondi 等人研究的 ( t − z ) 型平面波度量的曲率特性。1959 年。为此考虑了一般的 ( t - z ) 型波动度量，并获得了它遵守爱因斯坦空时空场方程的条件。发现(t-z)-型平面波度量的Ricci张量的秩为1且为Codazzi型。也证明了它不是复发而是Ricci复发，适形复发和超广义复发。此外，它是半对称的，并且满足 Ricci 广义伪对称类型条件 P ⋅ P = − 1 3 Q ( R ic , P ) 。有趣的是，在物理上，能量动量张量描述了一个具有平行射线的辐射场，在几何上它是一个 Codazzi 张量和半对称。作为特例，推导出了Taub平面对称时空度量的几何结构。观察 ( t - z ) 型平面波度量和 pp 波度量在其几何结构方面的比较。