Natural liftings of $(0,2)$-tensor fields to the tangent bundle
Doupovec, Miroslav
Archivum Mathematicum, Tome 030 (1994), p. 215-225 / Harvested from Czech Digital Mathematics Library

We determine all first order natural operators transforming $(0,2)$–tensor fields on a manifold $M$ into $(0,2)$–tensor fields on $TM$.

Publié le : 1994-01-01
Classification:  53A55,  53C15,  58A20
@article{107508,
     author = {Miroslav Doupovec},
     title = {Natural liftings of $(0,2)$-tensor fields to the tangent bundle},
     journal = {Archivum Mathematicum},
     volume = {030},
     year = {1994},
     pages = {215-225},
     zbl = {0816.53007},
     mrnumber = {1308355},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107508}
}
Doupovec, Miroslav. Natural liftings of $(0,2)$-tensor fields to the tangent bundle. Archivum Mathematicum, Tome 030 (1994) pp. 215-225. http://gdmltest.u-ga.fr/item/107508/

The canonical isomorphism between $T^kT^*M$ and $T^*T^kM$, CRAS Paris 309 (1989), 1509–1514. (1989) | MR 1033091

Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies 158, Amsterdam, 1989. (1989) | MR 1021489

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.

Natural transformations of the second tangent functor into itself, Arch. Math. (Brno) XX (1984), 169–172. (1984) | MR 0784868

Natural transformations of second tangent and cotangent functors, Czech. Math. J. 38(113) (1988), 274–279. (1988) | MR 0946296

Natural Operations in Differential Geometry, Springer-Verlag, 1993. (1993) | MR 1202431

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. (1987) | MR 0923348

Some results on second tangent and cotangent spaces, Quaderni dell’ Instituto di Matematica dell’ Università di Lecce Q. 16 (1978). (1978)

Liftings of tensor fields and connections to tangent bundle of higher order, Nagoya Math. J. 40 (1970), 99–120. (1970) | MR 0279719

Liftings of some types of tensor fields and connections to tangent bundles of $p^r$–velocities, Nagoya Math. J. 40 (1970), 13–31. (1970) | MR 0279720

Hamiltonian systems, Lagrangian systems and the Legendre transformation, Symp. Math. 14, 247–258, Roma 1974.

Tangent and cotangent bundles, Marcel Dekker Inc., New York, 1973. (1973) | MR 0350650