I don not know whether I was right or not, please give me a hint.
(R3,+) can be considered a Lie group. and its TG in 0 is still R3.
suppose X as a infinitesimal generater, it can give a left-invariant vector field and also an one-parameter subgroup.
but i think, this one-parameter...
Thank you, ystael!
I have found Spivak's calculus on manifolds and trying to read it.
and so sorry that there maybe a misunderstanding:
I know how to prove
dy^dx=-dx^dy
what i really confusing is why
dx^dy=dxdy
dy^dx=-dxdy
Is it only happened at R3?
I'm reading Marsden's vector calculus. In the chapter of differential forms, it mentions the wedge product satisfies the laws:
dy^dx=-dxdy.
and for a 0-form f, f^w=fw.
Does it have formal derivation?
hope someone can give me a hint or even a link.