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In this paper, we prove that a gradient shrinking Ricci soliton is rigid if the radial curvature vanishes and the second order divergence of Bach tensor is non-positive. Moreover, we show that a complete non-compact gradient expanding Ricci soliton is rigid if the radial curvature vanishes, the Ricci curvature is nonnegative and the second order divergence of Bach tensor is nonnegative.
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참고문헌 (13)
참고문헌 신청
B. L. Chen / 2009 / Strong uniqueness of the Ricci flow / J. Differential Geom 82 (2) : 363 ~ 382
G. Catino / / Gradient Ricci solitons with vanishing conditions on Weyl
G. Catino / / Rigidity of gradient Einstein shrinkers
H. D. Cao / 2009 / On complete gradient shrinking Ricci solitons / J. Differential Geom 85 (2) : 175 ~ 185
H. D. Cao / 2013 / On Bach-flat gradient shrinking Ricci solitons / Duke Math. J 162 (6) : 1149 ~ 1169
G. Catino / / Gradient Ricci solitons with vanishing conditions on Weyl
G. Catino / / Rigidity of gradient Einstein shrinkers
H. D. Cao / 2009 / On complete gradient shrinking Ricci solitons / J. Differential Geom 85 (2) : 175 ~ 185
H. D. Cao / 2013 / On Bach-flat gradient shrinking Ricci solitons / Duke Math. J 162 (6) : 1149 ~ 1169
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