Definition Let be a smooth -form on a smooth manifold , and let be a smooth vector field on . The contraction of with is the smooth -form that maps to . In other words, is point-wise evaluated with in the first slot. We shall denote this -form by . If is a -form, we set for all .
Properties Let and be as above. Then the following properties hold:
For any real number
For vector fields and
Contraction is an anti-derivation . If is a -form, and is a -form, then
- 1 T. Frankel, Geometry of physics, Cambridge University press, 1997.
|Date of creation||2013-03-22 13:37:28|
|Last modified on||2013-03-22 13:37:28|
|Last modified by||mathcam (2727)|