Let,
and
,
be two functions.
Ifare two manifolds of dimension
respectively and
a differentiable function, while
an open set. Let
be a point at
and
and
be the respective tangent spaces. We define
, where if
then
is differentiable at an area of
and for each
we have
Calculate a matrix ofand
. Then find the vector
Also ifis a differentiable bijection with
also differentiable and
are two vector fields onto M, then
,
are also vector fields onto N. Show that
where
is the Lie bracket.
If someone could explain me the definition a bit, as well as to solve this (simple, I think) problem I would be grateful!