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--- math214:home [2020/05/17 16:18]
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+++ math214:home [2020/12/18 21:23] (current)
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   * Week 11:
     * [[04-06]]: {{ :math214:note_6_apr_2020.pdf |ipad note}}Holonomy, interpretation of Curvature[Ni] 3.3.4
-      * Errata of ipad note: page 1, right column. It should be: if $A = \omega \ot (e_\alpha \ot \delta^\beta)$, for  $\omega \in \Omega^1(U)$  and  $e_\alpha$  the local frame of  $E$  previously chosen, and  $\delta^\beta$  the dual frame of  $E^*$ , then $dA = d(\omega) \ot (e_\alpha \ot \delta^\beta) $. This is because$ d e_\alpha =0, d \delta^\beta=0 $by the definition of local connection$ d $on$ E|_U$.
+      * Errata of ipad note: page 1, right column. It should be: if $A = \omega \otimes (e_\alpha \ot \delta^\beta)$, for  $\omega \in \Omega^1(U)$  and  $e_\alpha$  the local frame of  $E$  previously chosen, and  $\delta^\beta$  the dual frame of  $E^*$ , then $dA = d(\omega) \otimes (e_\alpha \ot \delta^\beta) $. This is because$ d e_\alpha =0, d \delta^\beta=0 $by the definition of local connection$ d $on$ E|_U$.
     * 04-08: {{ :math214:note_8_apr_2020.pdf |ipad note}} Connection on Tangent Space. Levi-Cevita connection.
     * 04-10: {{ :math214:note_10_apr_2020_3_.pdf | ipad note}}. Levi-Cevita connection for bi-invariant metric on Lie group. Begin Geodesic equation.

Lecture Notes