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Kobak, Piotr
Natural liftings of vector fields to tangent bundles of bundles of $1$-forms. (English). Mathematica Bohemica, vol. 116 (1991), issue 3, pp. 319-326
MSC: 53A55, 58A20 | MR 1126453 | Zbl 0743.53008 | DOI: 10.21136/MB.1991.126171
Keywords:
natural operators; vector fields; prolongation of the flow; natural liftings; equivariant maps; natural bundles
Summary:
Natural liftings $D:I\rightarrow ITT^*$ are classified for $n\geq 2$. It is proved that they form a 5-parameter family of operators.
References:
[1] D. J. Eck: Product-preserving functors on smooth manifolds. J. Pure Appl. Algebra 42 (1986), 133-140. DOI 10.1016/0022-4049(86)90076-9 | MR 0857563 | Zbl 0615.57019
[2] G. Kainz P. Michor: Natural transformations in differential geometry. Czechoslovak Math. J. 37 (112) (1987), 584-607. MR 0913992
[З] I. Kolář: On the natural operators on vector fields. Ann. Glob. Anal. Geom. 6 (1) (1988), 109-117. DOI 10.1007/BF00133034 | MR 0982760
[4] I. Kolář P. W. Michor J. Slovák: Natural operations in differential geometry. to appeaг.
[5] I. Kolář Z. Radziszewski: Natural transformations of second tangent and cotangent functors. Czechoslovak Math. J. 38 (113) (1988), 274-279. MR 0946296
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