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On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor

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 نشر من قبل Huai-Dong Cao
 تاريخ النشر 2020
  مجال البحث
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In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($nge 5$) complete $D$-flat gradient steady Ricci solitons. More precisely, we prove that any $n$-dimensional complete noncompact gradient steady Ricci soliton with vanishing $D$-tensor is either Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof extends to the shrinking case and the expanding case as well.



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