On the Topological Classification of Four-Dimensional Steady Gradient Ricci Solitons with Nonnegative Sectional Curvature

Yuehan Hao ()
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Yuehan Hao: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2025, vol. 13, issue 22, 1-14

Abstract: In this paper, we study the topology of steady gradient Ricci solitons with nonnegative sectional curvature. We apply a characterization theorem for the fundamental group of a positively curved steady gradient Ricci soliton that admits a critical point. As an application of the characterization theorem, we give a classification of the topology of complete four-dimensional steady gradient Ricci solitons with nonnegative sectional curvature.

Keywords: Ricci flow; Ricci soliton; topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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