- #1
yukcream
- 59
- 0
Q1 If given a 2D Riemannian space, ds^2 = dx^2 + x^2dy^2, do the componets of the metric tensor are these:
g_11 = 1, g_12 = 0
g_21 = o, g_22 = x^2 ?
In addition, I got a question from my lecturer:
Q2. 2 metrics, defined in a Riemannian space, are given by ds^2 = g_ijdx^idy^j
and ds'^2 = g'_ij dx^idy^j = e^z g_ijdx^idy^j , respectively, where z is a function of the coordinates x^i.
Find the relation between the Chritoffel symbols corresponding to the 2 two metrics~~~
I have no ideal how to solve it and what is e here? treat it as a function or is it represents the persudo tensor?
Can anyone help me~~
yukyuk
g_11 = 1, g_12 = 0
g_21 = o, g_22 = x^2 ?
In addition, I got a question from my lecturer:
Q2. 2 metrics, defined in a Riemannian space, are given by ds^2 = g_ijdx^idy^j
and ds'^2 = g'_ij dx^idy^j = e^z g_ijdx^idy^j , respectively, where z is a function of the coordinates x^i.
Find the relation between the Chritoffel symbols corresponding to the 2 two metrics~~~
I have no ideal how to solve it and what is e here? treat it as a function or is it represents the persudo tensor?
Can anyone help me~~
yukyuk