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Please help, construct a natural differential structure on this manifold

by saminator910
Tags: construct, differential, manifold, natural, structure
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saminator910
#1
Dec31-12, 11:01 AM
P: 94
I need to construct a natural smooth differential structure on the ellipsoid [(x^2)/(a^2)]+[(y^2)/(b^2)]+[(z^2)/(c^2)]=1
So I need an Atlas to produce this, how would I do this? I don't really have an idea of what functions and sets an Atlas consists of, can one use parametric equations? Also, is this diffeomorphic to S^2? There needs to be a smooth mapping from the ellipsoid to the 2-sphere, correct?
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