Abstract In this paper we have investigated the curvature restricted geometric properties of the generalized Kantowski-Sachs (briefly, GK-S) spacetime metric, a warped product of 2-dimensional base and 2-dimensional fibre. It is proved that GK-S metric describes a generalized Roter type, 2-quasi Einstein and E i n ( 3 ) manifold. It also has pseudosymmetric Weyl conformal tensor as well as conharmonic tensor and its conformal 2-forms are recurrent. Further, it realizes the curvature condition R ⋅ R = Q ( S , R ) + L ( t , θ ) Q ( g , C ) (see, Theorem 4.1 ). We have also determined the curvature properties of Kantowski-Sachs (briefly, K-S), Bianchi type-III and Bianchi type-I metrics which are the special cases of GK-S spacetime metric. The sufficient condition under which GK-S metric represents a perfect fluid spacetime has also been obtained.

中文翻译：

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Kantowski-Sachs 度量的曲率特性

摘要 在本文中，我们研究了广义 Kantowski-Sachs（简称 GK-S）时空度量的曲率限制几何特性，该度量是二维基础和二维纤维的翘曲乘积。证明了 GK-S 度量描述了广义 Roter 类型，2-拟爱因斯坦和 E 在（ 3 ）流形中。它还具有伪对称 Weyl 共形张量以及共谐张量，其共形 2-形式是循环的。此外，它实现了曲率条件 R ⋅ R = Q ( S , R ) + L ( t , θ ) Q ( g , C )（见定理 4.1）。我们还确定了 Kantowski-Sachs（简称为 KS）、Bianchi III 型和 Bianchi I 型度量的曲率特性，它们是 GK-S 时空度量的特例。也得到了 GK-S 度量代表完美流体时空的充分条件。