- #1
arroy_0205
- 129
- 0
I noticed somewhere the line element of a two-dimensional torus is written in the form
[tex]
ds^2=r^2(d\theta^2_1+d\theta^2_2)
[/tex]
The author only states that he assumes same radius parameter for simplicity and no further explanation is given. But I do not understand how that form is possible. I find, in such a case the line element should be
[tex]
ds^2=r^2 d\theta^2_1+r^2(1+\cos\theta_1)^2d\theta^2_2)
[/tex]
I cannot reduce this form to the first form. Can anyone explain how the first form for 2D line element of a torus is possible?
[tex]
ds^2=r^2(d\theta^2_1+d\theta^2_2)
[/tex]
The author only states that he assumes same radius parameter for simplicity and no further explanation is given. But I do not understand how that form is possible. I find, in such a case the line element should be
[tex]
ds^2=r^2 d\theta^2_1+r^2(1+\cos\theta_1)^2d\theta^2_2)
[/tex]
I cannot reduce this form to the first form. Can anyone explain how the first form for 2D line element of a torus is possible?