7 dec 2021 -- 14:30
DIMaI, Firenze (online)
Seminari di Geometria Differenziale e Analisi Complessa del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'Università di Firenze
Abstract.
The preservation of positive curvature conditions under the Ricci flow has been an important ingredient in applications of the flow to solving problems in geometry and topology. Works by Hamilton and others established that certain positive curvature conditions are preserved under the flow, culminating in Wilking's unified, Lie algebraic approach to proving invariance of positive curvature conditions. Yet, some questions remain. In this talk, we describe sec > 0 initial metrics on S4, where the condition of sec > 0 is not preserved under the Ricci flow. Previously, examples of such behaviour were known for sec \geq 0, and for sec > 0 in dimension 6 and above. This is joint work with Renato Bettiol.