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arXiv · 2303.17663

The curvature operator of the second kind in dimension three

Harry Fluck·Xiaolong Li
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Abstract

This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that $\a$-positive/$\a$-nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all $\a \in [1,5]$.

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Harry Fluck, Xiaolong Li. 2023-03-30. The curvature operator of the second kind in dimension three. https://arxiv.org/abs/2303.17663

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