- #1

- 368

- 58

## Homework Statement:

- All below ...

## Relevant Equations:

- \n

I would appreciate if someone check my work:

I tried to simplify the answer a lot: I imagined that, if we have this ds between two points different than the distance that should be if the space was flat, so it would be enough to generalize and say that space is not flat.

So, using this argument, i just analysed when ##\theta, \phi = \pi/2,0##. It would lead us to the ordinary "x" axis on the "xy plane".

So making r = 2, r =1, if the space is plane the distance between this points need to be 1.

##ds = \int_{1}^{2} \frac{r}{(r²+a²)^{1/2}}dr = (4+a²)^{1/2}-(1+a²)^{1/2} \neq 1## if ## a \neq 0##

Since a = 0 would be the ordinary spherical coordinates, the final answer is, yes, it is curved. Is it ok?