关键词: 半对称度量ρ-联络, 共形向量场, Yamabe孤立子, Weyl张量, Killing型向量场

Abstract: By using the properties of differential operators, covariant derivative operator, Lie-derivative operator and the expressions of curvature tensor fields on Riemannian manifold, we discussed the characteristics of n(n>3)-dimensional conformally flat Yamabe soliton with the semi-symmetric metric ρ-connection under compact condition, and gave a necessary and sufficient condition that sectional curvature of Yamabe sotion with this structure was constant. The results show that the sectional curvature of Yamabe soliton with this structure is constant -1, the soliton constant is -n(n-1), and the soliton field is a Killing vector field.

Key words: semi-symmetric metric ρ-connection, conformal vector field, Yamabe soliton, Weyl tensor, Killing vector field