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Coordinates of a manifold

by Shyan
Tags: coordinates, manifold
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Mar12-12, 08:23 AM
Shyan's Avatar
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I'm just learning manifold geometry and tensor analysis.From the things I've understood till now,an idea came into my mind but I can find it or its negation no where.So I came to ask it here.
I can't explain how I deduced this but I think there should be sth like a natural coordinate for a particular manifold.I mean sth that is the most suitable or maybe the only possible map for it to make an atlas.E.g. Cartesian coordinates for euclidean manifold and spherical polar coordinates for a spherical manifold.
And I should tell I've not even finished one book on manifold geometry so if I'm telling sth crazy here,I apologize.
Thanks in advance
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Mar12-12, 08:49 AM
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Fredrik's Avatar
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For some manifolds, there are coordinate systems that are "special" in some sense. But I don't think that anything like that holds in general.
Mar12-12, 09:30 AM
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There is no such thing as a canonically given atlas for any manifold Shyan, but there are some manifolds that come up often, like R^n, the circle, tori, CP^n on which there is an obvious choice of atlas. So much so that people won't bother specifying what atlas they are working with in these case, or they might refer to it as "the natural atlas". But it is only natural in the sense that it is convenient and widely used.

Mar12-12, 09:45 AM
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Coordinates of a manifold

thanks for the answers.
So could you take a look at .
thanks again

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