A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
Revision as of 17:56, 25 April 2020
, 25 April 2020→The Levi-Civita Connection
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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. | ||