Ragini Singhal, University of Münster
Solutions and singularities of the Ricci-harmonic flow and Ricci-like flows of G2-structures
We find explicit solutions and singularities of the Ricci-harmonic flow of $G_2$-structures on 7-dimensionalcontact Calabi-Yau manifolds and the 7-dimensional Heisenberg group. We prove that the natural co-closed$G_2$-structure on a contact Calabi-Yau manifold as the initial condition leads to an ancient solution of the Ricci-harmonic flow with a finite time Type I singularity. These are the first examples of Type I singularities of the Ricci-harmonic flow. We also obtain similar (but different) results for the Ricci-like flows of $G_2$-structures studied by Gianniotis--Zacharopoulos in arXiv:2505.06872 (J. Geom. Anal. 36.2 (2026)) and of the negative gradient flow of an energy functional of $G_2$-structures studied by Weiss--Witt. The talk is based on a joint work with Shubham Dwivedi (Hamburg).
MC 5417