Isometric flows of \(G_2\)-structures. (English) Zbl 07819144
Cerejeiras, Paula (ed.) et al., Current trends in analysis, its applications and computation. Proceedings of the 12th ISAAC congress, Aveiro, Portugal, July 29 – August 3, 2019. Cham: Birkhäuser. Trends Math., 545-553 (2022).
Summary: We survey recent progress in the study of flows of isometric \(G_2\)-structures on seven-dimensional manifolds, that is, flows that preserve the metric, while modifying the \(G_2\)-structure. In particular, heat flows of isometric \(G_2\)-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.
For the entire collection see [Zbl 1497.42002].
For the entire collection see [Zbl 1497.42002].
MSC:
| 53C10 | \(G\)-structures |
| 53C29 | Issues of holonomy in differential geometry |
| 58E30 | Variational principles in infinite-dimensional spaces |
| 58E15 | Variational problems concerning extremal problems in several variables; Yang-Mills functionals |
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