i have a proof of a statement, but i don't understand it very well. I have concrete questions about it and it would be very nice, when someone can help me.
Let E be a subbundle of TM, we define the (graded) ideal as follows for any sections of E
Claim: J is locally generated by q linearly independent 1-forms:
Pf: Choose a local frame of TM, s.t. form a frame of E.
There is the dual frame of differential 1-forms of TM* and the linearly independent 1-forms clearly generate the ideal J.
Why do they generate the Ideal J????
What does it mean "generate"? the are 1-forms, i.e. sections: .
and J is the direct sum of k-forms, for k=1,...,n?
Can you please explain it for me?