Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 2 / x

Table of contents
- Solution x

Solution

Antisymmetrize part ix in

a, b

. The left side vanishes because the second derivative is symmetric in

s, t

. Therefore

f^{c}_{ab} (y) = f^{c}_{ab} (z), f^{c}_{ab} = [T_{a} μ_{b}^{r} - T_{b} μ_{a}^{r}] λ_{r}^{c} .

Since multiplication by an arbitrary

g (x)

moves

y

to any

z

in the connected coordinate neighborhood, the

f^{c}_{ab}

are constants. They are the structure constants.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version