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arXiv · 2203.14916

On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons

Xu Cheng·Ernani Ribeiro Jr·Detang Zhou
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Abstract

In this article, we investigate the geometry of $4$-dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a $4$-dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.

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Xu Cheng, Ernani Ribeiro Jr, Detang Zhou. 2022-03-28. On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons. https://arxiv.org/abs/2203.14916

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