Positive Hermitian curvature flow on special linear groups and perfect solitons

Stanfield, James

doi:10.1090/proc/16188

Positive Hermitian curvature flow on special linear groups and perfect solitons
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by James Stanfield

Proc. Amer. Math. Soc. 151 (2023), 835-851

DOI: https://doi.org/10.1090/proc/16188

Published electronically: September 15, 2022

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Abstract:

We study invariant solutions to the positive Hermitian curvature flow, introduced by Ustinovskiy, on complex Lie groups. We show in particular that the canonical scale-static metrics on the special linear groups, arising from the Killing form, are dynamically unstable. This disproves a conjecture of Ustinovskiy. We also construct certain perfect Lie groups that admit at least two distinct invariant solitons for the flow, only one of which is algebraic. This is the second known example of a geometric flow with non-algebraic, homogeneous solitons. The first being the G2-Laplacian flow.

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