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

2022/03/28 by Cheng, Xu, Ribeiro, Ernani, Zhou, Detang · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.14916

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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