On the natural operators on vector fields

DOI10.1007/BF00133034zbMath0678.58003OpenAlexW2169203026MaRDI QIDQ1124179

No author found.

Publication date: 1988

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00133034

zbMATH Keywords

group functorflow prolongationgeneralized Liouville vector fieldsWeil-algebras

Mathematics Subject Classification ID

Jets in global analysis (58A20) Differential invariants (local theory), geometric objects (53A55)

Related Items (16)

Natural base-extending operators of foliations into foliations on the Weil functors ⋮ Lifts of some tensor fields and connections to product preserving functors ⋮ Bundle functors on fibred manifolds ⋮ The geometrical constructions lifting tensor fields of type (0,2) on manifolds to the bundles ofA-velocities ⋮ Lifting vector fields from manifolds to the $r$-jet prolongation of the tangent bundle ⋮ Natural bundles and operators ⋮ Torsions of connections on some natural bundles ⋮ Linear natural operators lifting p-vectors to tensors of type (q, 0) on Weil bundles ⋮ Some liftings of poisson structures to Weil bundles ⋮ Linear duals of graded bundles and higher analogues of (Lie) algebroids ⋮ Natural Operators Lifting Vector Fields to Bundles of Weil Contact Elements ⋮ Natural T-Functions on the Cotangent Bundle of a Weil Bundle ⋮ Unnamed Item ⋮ Linear liftings of skew symmetric tensor fields of type (1, 2) to Weil bundles ⋮ Some natural constructions on vector fields and higher order cotangent bundles ⋮ Complete lifting of double-linear semi-basic tangent valued forms to Weil like functors on double vector bundles

Cites Work

• Natural transformations of vector fields on manifolds to vector fields on tangent bundles
• Prolongation of connections to bundles of infinitely near points
• Natural bundles have finite order
• Differential geometry of higher order
• Natural operators transforming vector fields to the second order tangent bundle
• On the order of natural differential operators and liftings
• Product-preserving functors on smooth manifolds
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