| Title:
|
Local equivalence of some maximally symmetric $(2,3,5)$-distributions II (English) |
| Author:
|
Randall, Matthew |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
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1212-5059 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
9-41 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show the change of coordinates that maps the maximally symmetric $(2,3,5)$-distribution given by solutions to the $k=\frac{2}{3}$ and $k=\frac{3}{2}$ generalised Chazy equation to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric $k=\frac{2}{3}$ and $k=\frac{3}{2}$ generalised Chazy distribution and the flat Cartan or Hilbert-Cartan distribution. We give the set of vector fields parametrised by solutions to the $k=\frac{2}{3}$ and $k=\frac{3}{2}$ generalised Chazy equation and the corresponding Ricci-flat conformal scale that bracket-generate to give the split real form of $\mathfrak{g}_2$. (English) |
| Keyword:
|
(2,3,5)-distributions |
| Keyword:
|
generalised Chazy equation |
| MSC:
|
34A05 |
| MSC:
|
34A34 |
| MSC:
|
58A15 |
| MSC:
|
58A17 |
| DOI:
|
10.5817/AM2025-1-9 |
| . |
| Date available:
|
2025-03-24T13:07:06Z |
| Last updated:
|
2025-03-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152917 |
| . |
| Reference:
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