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Suppose, I know the metric tensor of a 2D space. for example, the metric tensor of a sphere of radius R,

g

,and I just know the metric tensor, but don't know that it is of a sphere.

Now I want to draw a 2D space(surface) which will have the metric tensor g

g

_{ij}= ##\begin{pmatrix} R^2 & 0 \\ 0 & R^2\cdot sin^2\theta \end{pmatrix}##,and I just know the metric tensor, but don't know that it is of a sphere.

Now I want to draw a 2D space(surface) which will have the metric tensor g

_{ij}and will be embedded on 3D Euclidean space.
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