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Vector-Valued Differential Forms

  • Luis A. Cordero
  • C. T. J. Dodson
  • Manuel de León
Part of the Mathematics and Its Applications book series (MAIA, volume 47)

Abstract

We propose to build on the development in Sections 1.3 and 1.4 concerning the object J p 1 V for a vector space V. As a vector space, it is isomorphic to (p + 1) copies of V and it induces a canonical embedding of Lie groups (cf. 1.4): j p : J p 1 Gl(V)→ Gl(J p 1 V). This embedding allows a lifting of linear representation of a Lie group G in V by the functor J p 1 . As candidates for V, we are particularly interested in tensor products of R n and its dual; these being the fibre types of the geometrically interesting tangent tensor bundles on an n-dimensional manifold. A V-valued function on a manifold M is a section of M × V; a V-valued r-form on M is a section of ⋀ r MTV. We see how these are lifted by J p 1 . Similarly, we consider the lifting of V-valued functions on FM and their associated G-structures.

Keywords

Vector Field Vector Bundle Linear Representation Tensor Field Canonical Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Luis A. Cordero
    • 1
  • C. T. J. Dodson
    • 2
  • Manuel de León
    • 3
  1. 1.Department of Geometry and TopologyUniversity of Santiago de CompostelaSpain
  2. 2.Department of MathematicsUniversity of LancasterUK
  3. 3.C.E.C.I.M.E.-C.S.I.C.MadridSpain

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