Colloquium: 3-dimensional Ricci solitons under biconformal deformations, Elsa Ghandour, Université de Valenciennes
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Ricci solitons have played a fundamental role in geometry in recent years. They arise as limiting solutions to the Ricci flow and are essential ingredient in the work of Hamilton and Perelman in resolving Thurston's geometrization conjecture. In this work, we study 3-dimensional Ricci solitons through biconformal deformations, a natural generalization of conformal deformations. There are two main objectives: the first one is to understand how rigid soliton metrics are, and the second objective is to understand how many distinct biconformal equivalence classes of metrics there are amongst the Ricci soliton metrics. Along the way, we construct new examples of complete solitons and establish their uniqueness.