The subset of the tensor bundle \(T^kT^*M\) consisting of alternating tensors is denoted by \(\Lambda^kT^*M\). A section on the alternating tensor space \(\Lambda^k(T^*(M))\) is called differential \(k\)-form, this is a (continuous) tensor field with alternating tensors as values.
Remarks
- The wedge product or the interior multiplication on a differential forms is defined point wise.
- A covector field is a differential 1-form.