Journal of Jilin University Science Edition ›› 2021, Vol. 59 ›› Issue (5): 1045-1049.
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PAN Peng, LIU Jiancheng
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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
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PAN Peng, LIU Jiancheng. Characteristics of Conformally Flat Yamabe Soliton with Semi-symmetric Metric ρ-Connection[J].Journal of Jilin University Science Edition, 2021, 59(5): 1045-1049.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2021/V59/I5/1045
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