Homogeneous generalized Ricci flow

Abstract: The generalized Ricci flow is the natural analogue of the Ricci flow in the setting of generalized Geometry and it has a deep connection with the pluriclosed flow, a geometric flow of pluriclosed Hermitian metrics. To serve as motivation for our work, I will firstly introduce the pluriclosed flow and state some open questions, finally stating the precise link with the generalized Ricci flow. Afterwards, I will focus on the study of the homogeneous generalized Ricci flow, discussing its long-time existence on solvable Lie groups and asymptotics in the nilpotent case, with a special focus on the consequences for the pluriclosed flow. All such results are obtained by means of a new interpretation of the generalized Ricci flow as a flow of Dorfman brackets and of the generalized Ricci curvature as the moment map of a suitable action on Dorfman brackets. This is a joint work with Ramiro Lafuente and James Stanfield.

differential geometry

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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