| Title:
|
Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles (English) |
| Author:
|
Shurygin, Vadim V. |
| Author:
|
Zubkova, Svetlana K. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
111-120 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The second order transverse bundle $T^2_{}M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra $\mathbb {D}^2$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general $\mathbb {D}^2$-smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a $\mathbb {D}^2$-smooth foliated diffeomorphism between two second order transverse bundles maps the lift of a foliated linear connection into the lift of a foliated linear connection. (English) |
| Keyword:
|
Foliation |
| Keyword:
|
transverse bundle |
| Keyword:
|
second order transverse bundle |
| Keyword:
|
projectable linear connection |
| Keyword:
|
Lie derivative |
| Keyword:
|
Weil bundle |
| MSC:
|
53C12 |
| MSC:
|
53C15 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1365.58003 |
| idMR:
|
MR3674605 |
| . |
| Date available:
|
2016-08-30T12:02:23Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145822 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
