contraction
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:
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1.
For any real number
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2.
For vector fields and
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3.
Contraction is an anti-derivation [1]. If is a -form, and is a -form, then
References
- 1 T. Frankel, Geometry of physics, Cambridge University press, 1997.
Title | contraction |
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Canonical name | Contraction |
Date of creation | 2013-03-22 13:37:28 |
Last modified on | 2013-03-22 13:37:28 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 4 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 15A75 |
Classification | msc 58A10 |