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arXiv · 2103.12796

Rigidity of Bach-flat gradient Schouten solitons

Valter Borges
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Abstract

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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Valter Borges. 2021-03-23. Rigidity of Bach-flat gradient Schouten solitons. https://arxiv.org/abs/2103.12796

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