Nearly $G_2$-manifolds and $G_2$-Laplacian co-flows
Abstract
Nearly $G_2$-structures define positive Einstein metrics in $7$ dimensions and are critical points, up to scale, for a geometric flow of co-closed $G_2$-structures with good analytic properties called the modified $G_2$-Laplacian co-flow. We introduce a suitable normalization of this flow so that nearly $G_2$-structures are stable under rescaling. However, we show that many nearly $G_2$-structures are unstable for this flow: specifically, all those naturally arising from 3-Sasakian geometry. In particular, we demonstrate that the standard nearly $G_2$-structure on the round 7-sphere is an unstable critical point with high index.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Volume
- 34
- Issue
- 3
- Pages
- 707–745
- Publication date
- 1 January 2026
- Language
- EN