| Title:
|
Natural liftings of $(0,2)$-tensor fields to the tangent bundle (English) |
| Author:
|
Doupovec, Miroslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
215-225 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We determine all first order natural operators transforming $(0,2)$–tensor fields on a manifold $M$ into $(0,2)$–tensor fields on $TM$. (English) |
| Keyword:
|
natural operator |
| Keyword:
|
tensor field |
| Keyword:
|
complete lift |
| Keyword:
|
vertical lift |
| MSC:
|
53A55 |
| MSC:
|
53C15 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0816.53007 |
| idMR:
|
MR1308355 |
| . |
| Date available:
|
2008-06-06T21:26:38Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107508 |
| . |
| Reference:
|
[1] Cantrijn, F., Crampin, M., Sarlet, W., Saunders, D.: The canonical isomorphism between $T^kT^*M$ and $T^*T^kM$.CRAS Paris 309 (1989), 1509–1514. MR 1033091 |
| Reference:
|
[2] de León, M., Rodrigues, P.R.: Methods of Differential Geometry in Analytical Mechanics.North-Holland Mathematics Studies 158, Amsterdam, 1989. MR 1021489 |
| Reference:
|
[3] Janyška, J.: Natural $2$–forms on the tangent bundle of a Riemannian manifold.to appear in Proc. of Winter School in Srní, Suppl. Rend. Circ. Matem. Palermo. |
| Reference:
|
[4] Kolář, I.: Natural transformations of the second tangent functor into itself.Arch. Math. (Brno) XX (1984), 169–172. MR 0784868 |
| Reference:
|
[5] Kolář, I., Radziszewski, Z.: Natural transformations of second tangent and cotangent functors.Czech. Math. J. 38(113) (1988), 274–279. MR 0946296 |
| Reference:
|
[6] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[7] Kowalski, O., Sekizawa, M.: Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles – a classification.Differential Geometry and Its Applications, Proceedings, D. Reidel Publishing Company (1987), 149–178. MR 0923348 |
| Reference:
|
[8] Modugno, M., Stefani, G.: Some results on second tangent and cotangent spaces.Quaderni dell’ Instituto di Matematica dell’ Università di Lecce Q. 16 (1978). |
| Reference:
|
[9] Morimoto, A.: Liftings of tensor fields and connections to tangent bundle of higher order.Nagoya Math. J. 40 (1970), 99–120. MR 0279719 |
| Reference:
|
[10] Morimoto, A.: Liftings of some types of tensor fields and connections to tangent bundles of $p^r$–velocities.Nagoya Math. J. 40 (1970), 13–31. MR 0279720 |
| Reference:
|
[11] Tulczyjev, W.M.: Hamiltonian systems, Lagrangian systems and the Legendre transformation.Symp. Math. 14, 247–258, Roma 1974. |
| Reference:
|
[12] Yano, K., Ishihara, S.: Tangent and cotangent bundles.Marcel Dekker Inc., New York, 1973. MR 0350650 |
| . |
