2023/05/16 by Robert L. Bryant, Bryant, Robert L.
Mathematics · Physics and Astronomy · #53C29 #53E99 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2305.09772
openalex publication_date 2023/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The local generality of the space of solitons for the Laplacian flow of closed G2-structures is analyzed, and it is shown that the germs of such structures depend, up to diffeomorphism, on 16 functions of 6 variables (in the sense of E. Cartan). The method is to construct a natural exterior differential system whose integral manifolds describe such solitons and to show that it is involutive in Cartan's sense, so that Cartan-Kahler theory can be applied. Meanwhile, it turns out that, for the more special case of gradient solitons, the natural exterior differential system is not involutive, and the generality of these structures remains a mystery.