Isometric flows of G₂-structures

2020/08/14 by Sergey Grigorian, Grigorian, Sergey
Mathematics · #53C10 #53C29 #58E15 #58E30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2008.06593

openalex publication_date 2020/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey recent progress in the study of flows of isometric G₂-structures on 7-dimensional manifolds, that is, flows that preserve the metric, while modifying the G₂-structure. In particular, heat flows of isometric G₂-structures have been recently studied from several different perspectives, in particular in terms of 3-forms, octonions, vector fields, and geometric structures. We will give an overview of each approach, the results obtained, and compare the different perspectives.

Related

• Geometric Flows of G₂ Structures
• BRIDGES Lectures: Flows of geometric structures, especially G₂-structures
• Flows of co-closed G₂-structures
• Flows of conformally coclosed G₂-structures with dilaton
• Flows of G₂-structures, II: Curvature, torsion, symbols, and functionals