Abstract We characterize the three-dimensional Riemannian manifolds equipped with a semi-symmetric metric ρ -connection under the assumption that the Riemannian metric is a Yamabe soliton. It is shown that a three-dimensional Riemannian manifold endowed with a semi-symmetric ρ -connection, whose metric is Yamabe soliton, is a manifold of constant sectional curvature − 1 and the Yamabe soliton is expanding with soliton constant − 6 . Finally, we give an example of a three-dimensional Riemannian manifold and validate our findings.

中文翻译：

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具有一种允许 Yamabe 孤子的半对称度量连接的三维黎曼流形的表征

摘要 我们在黎曼度量是 Yamabe 孤子的假设下表征了配备有半对称度量 ρ -连接的三维黎曼流形。结果表明，具有半对称 ρ -连接的三维黎曼流形，其度量为 Yamabe 孤子，是一个截面曲率不变的流形 - 1 并且 Yamabe 孤子以孤子常数 - 6 膨胀。最后，我们给出了一个三维黎曼流形的例子并验证了我们的发现。