https://neckpinch.com/authors/aaron-kennon/New arXiv papers by Aaron Kennon, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2511.20773/arxiv:2511.20773Tue, 25 Nov 2025 00:00:00 GMTAaron Kennon, Jeffrey Streets — String backgrounds, defined here as metric connections with skew-symmetric torsion and reduced holonomy, yield generalized Ricci solitons relative to the Lee vector field. By a variational argument using the string action, they are also gradient generalized Ricci solitons relative to a potential function. These two observations combine to yield a canonical symmetry, and in this work we derive fundamental features of the transverse geometry, and rigidity phenomena. We prove in a unified conceptual fashion that the transverse geometry satisfies the string generalized Ricci soliton equations (a simplified Hull-Strominger system) in many settings including almost Hermitian, almost contact, SU(3), G₂, and Spin(7) geometry. We also show that the transverse geometry is always conformally co-closed, with the conformal factor given by the associated soliton potential.Generalized & G₂ flowsRicci solitonsStability & uniquenessSasakian & contact geometry https://neckpinch.com/papers/2210.12962/arxiv:2210.12962Mon, 24 Oct 2022 00:00:00 GMTAaron Kennon, Jason D. Lotay — 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.Ricci flowGeneralized & G₂ flowsEinstein metricsStability & uniquenessSasakian & contact geometry