Q1 If given a 2D Riemannian space, ds^2 = dx^2 + x^2dy^2, do the componets of the metric tensor are these:(adsbygoogle = window.adsbygoogle || []).push({});

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 any one help me~~

yukyuk

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# 2 Metric tensor question~

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