| Title:
|
Connections induced by $(1,1)$-tensor fields on cotangent bundles (English) |
| Author:
|
Dekrét, Anton |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
317-331 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
On cotangent bundles the Liouville field, the Liouville 1-form $\varepsilon$ and the canonical symplectic structure d$\varepsilon$ exist. In this paper interactions between these objects and ${(1,1)}$-tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated. (English) |
| Keyword:
|
connection |
| Keyword:
|
almost complex structure |
| Keyword:
|
tensor field |
| Keyword:
|
Liouville field |
| Keyword:
|
canonical symplectic structure |
| MSC:
|
53B05 |
| MSC:
|
53C05 |
| MSC:
|
53D05 |
| MSC:
|
58A20 |
| MSC:
|
58F05 |
| MSC:
|
70H35 |
| idZBL:
|
Zbl 0934.53020 |
| idMR:
|
MR1645458 |
| DOI:
|
10.21136/MB.1998.126068 |
| . |
| Date available:
|
2009-09-24T21:32:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126068 |
| . |
| Reference:
|
[1] Cabras A., Kolář I.: Special tangent valued forms and the Frölicher-Nijenhuis bracket.Arch. Math. (Brno) 29 (1993), 71-82. Zbl 0801.53014, MR 1242630 |
| Reference:
|
[2] Dekrét A.: On almost complex structures on fibre bundles.Acta Univ. M. Belii Math. 3 (1995), 3-8. Zbl 0856.53026, MR 1409884 |
| Reference:
|
[3] Doupovec M., Kurek J.: Liftings of tensor fields to the cotangent bundle.Proc. Conf. Diff. Geometry Brno 1995. Masaryk University, Brno, 1996, p. 141-150. MR 1406334 |
| Reference:
|
[4] Janyška J.: Remarks on the Nijenhuis tensor and almost complex connections.Arch. Math. (Brno) 26 (1990), 229-240. Zbl 0738.53014, MR 1188975 |
| Reference:
|
[5] Klein J.: On variational second order differential equations Polynomial case.Proc. Conf. Diff. Geometry and its Applications 1992. Silesian University, Opava, 1993, p. 449-459. MR 1255561 |
| Reference:
|
[6] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[7] Yano K.: Differential Geometry on Complex and Almost Complex Spaces.Pergamon Press, New York, 1965. Zbl 0127.12405, MR 0187181 |
| Reference:
|
[8] Yano K., Ishihara S.: Tangent and Cotangent Bundles.M. Dekker Inc., New York, 1973. Zbl 0262.53024, MR 0350650 |
| . |
