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Want to know (i) what does Riemannian metric tensor and Christoffel symbols on R

^{2}mean? (ii) How does metric tensor and Christoffel symbols look like on R

^{2}? It would be great with an example as I am new to this Differential Geometry.

- Thread starter shanky
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Want to know (i) what does Riemannian metric tensor and Christoffel symbols on R

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Thanks Orodruin.

But I want metric tensor(MT) and Christoffel symbols(CS) in R

What do you mean by choosing coordinate system ? Is it world / Cartesian coordinate system you mean?

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In order to express the components of the metric and the Christoffel symbols you need to select the coordinate system in which you want to find the components.

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3D object in Riemannian Space ..... real vector space with D=2 dimensions

In order to express the components of the metric and the Christoffel symbols you need to select the coordinate system in which you want to find the components.

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A manifold in general is not a vector space - its tangent spaces are.

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Yah its manifold - tangent spaces. My main question was what does Riemannian metric tensor and Christoffel symbols on R2 mean? Illustrate with example

A manifold in general is not a vector space - its tangent spaces are.

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Your question is still not very clear.

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