Vector-valued differential form: Difference between revisions

Revision as of 04:34, 8 January 2016

Revision as of 11:17, 13 March 2016

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where the latter two tensor products are the [[tensor product of modules]] over the [[ring (mathematics)|ring]] Ω⁰(''M'') of smooth '''R'''-valued functions on ''M'' (see the seventh example [[module (mathematics)#Examples|here]]). By convention, an ''E''-valued 0-form is just a section of the bundle ''E''. That is,

:<math>\Omega^0(M,E) = \Gamma(E).\,</math>

Equivalently, aan ''E''-valued differential form can be defined as a [[vector bundle morphism|bundle morphism]]

:<math>TM\otimes\cdots\otimes TM \to E</math>

which is totally [[skew-symmetric matrix|skew-symmetric]].