Journal of Jilin University Science Edition ›› 2021, Vol. 59 ›› Issue (3): 489-496.
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WEI Peixi, LIU Jiancheng
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Abstract: We discussed the rigidity of almost Ricci solitons by calculating the X-Laplacian for the module square of the trace-free curvature tensor. Under the assumption that the scalar curvature was nonnegative, we proved that a complete almost Ricci solitons were isometric to a finite quotient of Rn or Sn under a pointwise pinching condition. For a compact almost Ricci soliton, we gave an integral inequality and proved that the equal sign held if and only if the soliton was isometric to a finite quotient of Sn under the assumption that the scalar curvature was positive.
Key words: almost Ricci solitons, rigidity, X-Laplacian
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WEI Peixi, LIU Jiancheng. Rigidity of Almost Ricci Solitons[J].Journal of Jilin University Science Edition, 2021, 59(3): 489-496.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2021/V59/I3/489
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