Quadratic closed G2-structures

Abstract: I will talk about closed G2-structures satisfying the quadratic condition, a second-order PDE system introduced by Bryant involving a parameter. For particular special values of the parameter, the quadratic condition is equivalent to the Einstein equation, the extremally Ricci-pinched (ERP) condition, and the eigenform condition. I will describe my recent existence and classification results about these structures, including the first example of a complete inhomogeneous ERP G2-structure, a new compact ERP G2-structure, and the first examples of solutions to this PDE system for certain values of the parameter. If time permits, I will describe a related construction of complete inhomogeneous gradient solitons for the G2 Laplacian flow.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

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

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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