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Topic: How do we Evaluate This Form on S^1?
Replies: 11   Last Post: Jan 22, 2013 4:17 PM

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Shmuel (Seymour J.) Metz

Posts: 3,473
Registered: 12/4/04
Re: How do we Evaluate This Form on S^1?
Posted: Jan 21, 2013 7:28 AM
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In <x5qdnfD8tJNRFmHNnZ2dnUVZ5tidnZ2d@giganews.com>, on 01/20/2013
at 04:28 PM, "W. Dale Hall" <wdhall@alum.mit.edu> said:

>A tangent vector isn't *really* a real number

That much is true.

>[after all, tangent vectors to different points on S^1 aren't
>quite identifiable with one another since they belong to different
>tangent spaces],

That's a non sequitur and, in fact, is false. The standard affine
connection on S^1 is flat, so parallel transport establishes an
isomorphism between T_x and T_y, for x and y is S^1.

Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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