| Title:
|
The Tanaka-Webster connection for almost $\mathcal{S}$-manifolds and Cartan geometry (English) |
| Author:
|
Lotta, Antonio |
| Author:
|
Pastore, Anna Maria |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
47-61 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a CR-integrable almost $\mathcal S$-manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost $\mathcal S$-structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost $\mathcal S$-structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal almost $\mathcal S$-manifolds with higher CR-codimension, whose Tanaka–Webster curvature vanishes. (English) |
| Keyword:
|
almost $\mathcal S$-structure |
| Keyword:
|
Tanaka–Webster connection |
| Keyword:
|
Cartan connection |
| Keyword:
|
CR manifold |
| MSC:
|
32V05 |
| MSC:
|
53B05 |
| MSC:
|
53C10 |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 1114.53022 |
| idMR:
|
MR2054872 |
| . |
| Date available:
|
2008-06-06T22:42:54Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107890 |
| . |
| Reference:
|
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| . |
