Laplacian solitons: questions and homogeneous examples

Abstract

We give the first examples of closed Laplacian solitons which are shrinking, and in particular produce closed Laplacian flow solutions with a finite-time singularity. Extremally Ricci pinched G2-structures (introduced by Bryant) which are steady Laplacian solitons have also been found. All the examples are left-invariant G2-structures on solvable Lie groups.

14 pages

References in corpus (2)

• Laplacian Solitons and Symmetry in G_2-geometry
• Einstein locally conformal calibrated $G_2$-structures