Nearly $G_2$-manifolds and $G_2$-Laplacian co-flows

Jason D. Lotay; Jakob Stein

doi:10.4310/CAG.260813122441

paper

Nearly $G_{2}$ -manifolds and $G_{2}$ -Laplacian co-flows

arXiv:2505.14121 · doi:10.4310/CAG.260813122441

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.

20 pages. v2: minor changes, typos corrected, more references added. To appear in CAG

Nearly G2​-manifolds and G2​-Laplacian co-flows

Abstract

Nearly $G_{2}$ -manifolds and $G_{2}$ -Laplacian co-flows