| Title:
|
Curvature and the equivalence problem in sub-Riemannian geometry (English) |
| Author:
|
Grong, Erlend |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
58 |
| Issue:
|
5 |
| Year:
|
2022 |
| Pages:
|
295-327 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples, which are Engel (2,3,4)-manifolds, contact manifolds and Cartan (2,3,5)-manifolds. These notes are an edited version of a lecture series given at the 42nd Winter school: Geometry and Physics, Srní, Czech Republic, mostly based on [8] and other earlier work. However, the work on Engel (2,3,4)-manifolds is original research, and illustrate the important special case were our model has the minimal set of isometries. (English) |
| Keyword:
|
sub-Riemannian geometry |
| Keyword:
|
equivalence problem |
| Keyword:
|
frame bundle |
| Keyword:
|
Cartan connection |
| Keyword:
|
flatness theorem |
| MSC:
|
53C17 |
| MSC:
|
58A15 |
| idZBL:
|
Zbl 07655750 |
| idMR:
|
MR4529821 |
| DOI:
|
10.5817/AM2022-5-295 |
| . |
| Date available:
|
2022-11-28T12:32:33Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151156 |
| . |
| Reference:
|
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