Vector-valued differential form: Difference between revisions

Revision as of 04:42, 15 December 2014

Revision as of 04:46, 15 December 2014

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:<math>\Gamma(M, E) \to \{ f: P \to V | f(ug) = \rho(g)^{-1}f(u) \}, \, \overline{f} \mapsto f</math>.

Example: Let ''E'' be the tangent bundle of ''M''. Then identity bundle map id_''E'': ''E'' →''E'' is an ''E''-valued one form on ''M''. The [[tautological one-form]] is a unique one-form on the frame bundle of ''E'' that corresponds to id_''E''. Denoted by θ, it is a tensorial form of standard type. <!--The [[exterior covariant derivative]] of θ, Θ = ''D''θ is called a [[torsion form]].-->

==Notes==