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A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

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<p>[01:19:40] So it's now time to trade the family cow for the magic beans and bring them home and see whether or not we got the better of the deal.
<p>[01:19:40] So it's now time to trade the family cow for the magic beans and bring them home and see whether or not we got the better of the deal.


===== The Levi-Civita Connection =====
====== The Levi-Civita Connection ======
<p>[01:20:01] Okay. What is it that we get for the Levi-Civita connection? Well, not much. One thing we get is that normally the space of connections is an affine space. Not a vector space, but an affine space. Almost a vector space, a vector space up to a choice of origin. But with the Levi-Civita connection, rather than having an infinite plane with an ability to take differences, but no real ability to have a group structure.
<p>[01:20:01] Okay. What is it that we get for the Levi-Civita connection? Well, not much. One thing we get is that normally the space of connections is an affine space. Not a vector space, but an affine space. Almost a vector space, a vector space up to a choice of origin. But with the Levi-Civita connection, rather than having an infinite plane with an ability to take differences, but no real ability to have a group structure.


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