A class of eternal solutions to the G${}_2$-Laplacian flow

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.

17 pages. To appear in The Journal of Geometric Analysis

References in corpus (2)

• Curvature decomposition of G_2 manifolds
• On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

Cited by in corpus (5)

• A new example of a compact ERP G2-structure
• $S^1$-invariant Laplacian flow
• Remarks on homogeneous solitons of the G${}_2$-Laplacian flow
• Curvature pinching estimate under the Laplacian G_{2} flow
• Real analyticity of the modified Laplacian coflow