TL;DR
This paper discusses specific types of Ricci solitons, including gradient Ricci solitons and their relation to Einstein and Kähler-Ricci solitons, providing a detailed mathematical classification and description.
Contribution
It offers a detailed analysis of Ricci solitons, including Perelman's proof of their gradient nature in compact cases and a unified description of related Einstein and Kähler-Ricci solitons.
Findings
Perelman's proof of gradient Ricci solitons for compact cases
Unified description of Einstein and Kähler-Ricci solitons
Classification of Ricci solitons arising from conformal changes
Abstract
English translation of "Solitony Ricciego" (Wiadomo\'sci Matematyczne 48, 2012, no. 1, pp. 1-32). Despite the general-sounding title, the text covers just a few narrow topics: Perelman's proof of the fact that compact Ricci solitons are of the gradient type, and a detailed unified description of Page's and Berard Bergery's Einstein manifolds on the one hand, and Koiso's and Cao's K\"ahler-Ricci solitons on the other, as the Ricci solitons arising via conformal changes from certain special K\"ahler manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds