An upper diameter bound for compact Ricci solitons with applications to the Hitchin-Thorpe inequality

2015/04/21 by Tadano, Homare · 1 citation
#53C25 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C21 #Secondary 53C20

paper · doi:10.48550/arxiv.1504.05577

Abstract

In this article, stimulated by Fernandez-Lopez and Garcia-Rio, we shall give an upper diameter bound for compact Ricci solitons in terms of the range of the scalar curvature. As an application, we shall provide some sufficient conditions for four-dimensional compact Ricci solitons to satisfy the Hitchin-Thorpe inequality.

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• Gradient Shrinking Ricci Solitons and Modified Sectional Curvature

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