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A gradient flow of Spin(7)-structures
Published 1 Apr 2024 in math.DG | (2404.00870v1)
Abstract: We formulate and study the negative gradient flow of an energy functional of Spin(7)-structures on compact 8-manifolds. The energy functional is the $L2$-norm of the torsion of the Spin(7)-structure. Our main result is the short-time existence and uniqueness of solutions to the flow. We also explain how this negative gradient flow is the most general flow of Spin(7)-structures. We also study solitons of the flow and prove a non-existence result for compact expanding solitons.
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