| Title:
|
On $(1,1)$-tensor fields on symplectic manifolds (English) |
| Author:
|
Dekrét, Anton |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
329-336 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Two symplectic structures on a manifold $M$ determine a (1,1)-tensor field on $M$. In this paper we study some properties of this field. Conversely, if $A$ is (1,1)-tensor field on a symplectic manifold $(M, \omega )$ then using the natural lift theory we find conditions under which $\omega ^A, \omega ^A(X, Y)=\omega (AX, Y)$, is symplectic. (English) |
| Keyword:
|
symplectic structure |
| Keyword:
|
natural lifts on tangent and cotangent bundles |
| MSC:
|
37J05 |
| MSC:
|
53D05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 1054.53089 |
| idMR:
|
MR1744520 |
| . |
| Date available:
|
2008-06-06T22:24:46Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107707 |
| . |
| Reference:
|
[1] Doupovec, M., Kurek, J.: Liftings of tensor fields to the cotangent bundle.Proceedings, Int. conference Diff. Geometry and Applications Brno (1996), MU Brno, 141–150. MR 1406334 |
| Reference:
|
[2] Doupovec, M., Kurek, J.: Liftings of covariant (0,2)-tensor fields to the bundle of $k$-dimensional 1-velocities.Supplements di Rendiconti del Circolo Matematico di Palermo, Serie II 43 (1996), 111–121. MR 1463514 |
| Reference:
|
[3] Gancarzewicz, J., Mikulski, W., Pogoda, Z.: Lifts of some tensor fields and connections to product preserving functors.135 (1914), Nagoya Math. J., 1–41. MR 1295815 |
| Reference:
|
[4] Libermann, P., Marle, Ch.: Symplectic Geometry and Analytical Mechanics.(1987), D. Reider Pub. Comp., Dortrecht - Boston - Lancaster - Tokyo. MR 0882548 |
| Reference:
|
[5] Yano, K., Ishihara, S.: Tangent and cotangent bundles.M. Dekker Inc. New York, 1973. MR 0350650 |
| . |
