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Definition: Differential Form of Degree k

Let M be a differentiable manifold. A differential form of degree k is a section of the n-th alternating product of its cotangent bundle, i.e. it is a function

\omega \colon \cases{M\longrightarrow \bigwedge ^{k}T^{ * }M,\\x\longmapsto \omega (x),}

with \omega (x)\in \bigwedge ^{k}T_{x}^{ * }M.


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References

Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück