Generalized Ricci flow and its solitons in complex geometry

Abstract: Generalized Ricci flow is a natural flow coupling the Ricci flow with an evolution equation for a closed 3-form. This flow emerges in two different settings in complex geometry expanding the applicability of the Ricci flow beyond the world of Kähler manifolds. The purpose of the talk is to explain how the steady soliton equations for this flow give rise to the notions of canonical metrics in non-Kähler and bi-Hermitian complex geometry. The corresponding differential equations have been long known in physics, so the description and classification of compact/complete solutions is of great interest. We show how the rich complex-geometric structure of the underlying manifolds allows for the adaptation of many methods of the Kähler geometry to the study of the Generalized Ricci flow and its solitons.

algebraic geometryanalysis of PDEsdifferential geometry

Audience: researchers in the topic

Geometry & TACoS - Session VIII : Complex Geometric Flows

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