pervect, we have two variables inside the brackets, a and b.
ok... but see the curvature tensor:
R_{a}_{[b}_{c}_{d]}=0
it is definition equal of the tensor antisymmetric in the brackets?
(where it origines ∂[aΓdb]c = ½(∂aΓdbc - ∂bΓdac) ? )
thank very much!
R_{a}_{b}_{c}^{d}ω_{d}=((-2)\partial_{[a}\Gamma^{d}_{b] }_{c}+2\Gamma^{e}_{[a]}_{c}\Gamma^{d}_{[b]}_{e})ω_{d}
good, me question is about of:
1.- as appear the coefficient (-2) und the (2)?
2.- it is assumed that...
i apologize for the delay, here is the proof:
F:ℝ^{n}\rightarrowℝ
i have:
F(\vec{x})-F(\vec{a})= \sum^{m}_{μ=1}F(t(x^{μ}-a^{μ})+a^{μ},0...,0)^{t=1}_{t=0}
then:
=\sum^{m}_{μ=1}(x^{μ}-a^{μ})\int^{1}_{0}\frac{\partial F}{\partial u^{μ}}((t(x^{μ}-a^{μ})+a^{μ},0...,0)dt
where...
Fredrick thank you very much, the book is recommended to study this issue, although the theorem is raised from other values is the same. thank!
ps: "Modern Differential Geometry for Physicists" autor: Isham
hello!:
my problem is about of a theorem mathematic,as I prove the following theorem?
F(x)=F(a) + \sum^{n}_{i=1}(x^{i}-a^{i})H_{i}(x)
good first start with the fundamental theorem of calculus: (for proof):
F(x) - F(a) = \int^{x}_{a}F'(s)ds sustitution: s=t(x - a) + a...
I wanted to delete the entire message but could not, my reason was that I answered my questions, was a simple "binomial series." Anyway I upload issue again.
thank you very much.
Hello!:
My name is Camilo, i want answer one question about of special relativity, in Landau volumen II.
the question is in doc attachments!
is my first time, sorry.