Hi.
I have a question on proof of proposition 2 in chater 7 Spivak volume2.
In the proof, he says that the n-dimensional distribution
\Delta_{p}=\bigcap^{n}_{i,j=1}ker\Lambda^{i}_{j}(p)
in R^(n+n^2) is integrable.
Could anyone explain why it is an n dimensional distribution?
Thanks.
Let Y_{1},..,Y_{k} be vector fields and let A be a tensor field of type ^{k}_{1}. Could you explain how applying k contractions to A\otimesY_{1}\otimes...Y_{k} yields A(Y_{1}...Y_{k})?
Actually, could you first explain why contraction of w\otimesY is equal to w(Y)?
Here, w is a 1-form and Y...
I am using third edition the page number is 220 221.
I don't know how to use latex. But the equation involves the relationship between \Gamma^{'\gamma}_{\alpha\beta} and \Gamma^{k}_{ij}
In page 221, He also says:
A (classical) connection on a manifold M is an assignment if n^3 numbers to each...