We explicitly describe the solution of the G_2-Laplacian flow starting from an extremally Ricci-pinched closed G_2-structure on a compact 7-manifold and we investigate its properties. In particular, we show that the solution exists for all real times and that it remains extremally Ricci-pinched. This result holds more generally on any 7-manifold whenever the intrinsic torsion of the extremally Ricci-pinched G_2-structure has constant norm. We also discuss various examples.
A Class of Eternal Solutions to the G_2-Laplacian Flow
Fino, Anna;Raffero, Alberto
2021-01-01
Abstract
We explicitly describe the solution of the G_2-Laplacian flow starting from an extremally Ricci-pinched closed G_2-structure on a compact 7-manifold and we investigate its properties. In particular, we show that the solution exists for all real times and that it remains extremally Ricci-pinched. This result holds more generally on any 7-manifold whenever the intrinsic torsion of the extremally Ricci-pinched G_2-structure has constant norm. We also discuss various examples.
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