Bach平坦梯度Schouten孤子的刚性
Rigidity of Bach-flat gradient Schouten solitons
摘要：
本文证明了当完备Schouten孤子的Ricci张量在每一点至多有两个本征值时，它是刚性的。这使得收缩和膨胀巴赫平坦Schouten孤子的$n\geq$ 4的分类。当$n=3$时，我们能够在更一般的条件下得出刚性的结论，即当巴赫张量是发散自由的时候。这些结果暗示了$n\geq3$的局部共形平坦Schouten孤子的刚性。
英文摘要：
In this paper we show that a complete Schouten soliton whose Ricci tensor has at most two eigenvalues at each point is rigid. This allows the classification of both shrinking and expanding Bach-flat Schouten solitons for $n\geq$ 4. When $n=3$ we are able to conclude rigidity under a more general condition, namely when the Bach tensor is divergence free. These results imply rigidity of locally conformally flat Schouten solitons for $n\geq3$.
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