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Topology/Geometry Seminar

On the Stability of 3-Sasakian Nearly Parallel G2-Structures

Aaron Kennon (UC Santa Barbara/ Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics)

Location:  Hill Center, Room 705
Date & time: Tuesday, 13 December 2022 at 4:00PM - 5:00PM

A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel G2-structures which may also be expressed in terms of the 3-Sasakian structure. Just as Einstein metrics are critical points for the Ricci flow up to rescaling, nearly parallel G2-structures provide natural critical points of the (rescaled) geometric flows of G2-structures known as the Laplacian flow and Laplacian coflow. We study each of these flows in the 3-Sasakian setting and see that their behaviour is markedly different, particularly regarding the stability of the nearly parallel G2-structures. We also compare the behaviour of the flows of G2-structures with the (rescaled) Ricci flow. This was joint work with Jason Lotay.