Talk:Fundamental vector field

Is it sure, that $$ d $$ is an exterior derivative in the definition? Not a Pushforward (differential)?

89.135.19.250 (talk) 17:47, 30 November 2013 (UTC)


 * Why do you use "pushfoward"? If G is acting on X, then let $$f(g) = g \cdot x$$ so $$f: G \to X$$ and differentiating this (i.e., exterior derivative) we get: $$df_1: T_1 G = \mathfrak{g} \to T_x X$$. Varying x you get a fundamental vector field. (I'm not sure why the article is using strange notations.) -- Taku (talk) 19:14, 30 November 2013 (UTC)
 * I don't understand this. Why do you say "differentiating this (i.e., exterior derivative)"? Is any relationship between differential (i.e the tangent map) and the exterior derivative (i.e. an operation that assigns a (k+1) -form to a k-form)? 89.135.19.250 (talk) 20:04, 30 November 2013 (UTC)
 * Ah, I see you're thinking of differential forms. No, "d" here is not that exterior derivative. I have changed the wording accordingly. -- Taku (talk) 00:33, 1 December 2013 (UTC)