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Graph, Wall, Tome: Difference between revisions

202 bytes added ,  29 January 2020
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$$dV^{3} = dX^{1}dX^{2} (V^{1}R^{3}_{112} + V^{2}R^{3}_{212} + V^{3}R^{3}_{312})$$
$$dV^{3} = dX^{1}dX^{2} (V^{1}R^{3}_{112} + V^{2}R^{3}_{212} + V^{3}R^{3}_{312})$$


or, using $$i$$ to summarize across all 3 components (difference vectors):
or, using $$i$$ to summarize across all 3 components (difference vectors):
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$$dV^{i} = dX^{1}dX^{2} \Sigma_{j} [(V^{j}R^{i}_{j12}]$$
$$dV^{i} = dX^{1}dX^{2} \Sigma_{j} [(V^{j}R^{i}_{j12}]$$


* See: [https://www.youtube.com/watch?v=UfThVvBWZxM&t=19m33s the video @ 19m33s]
See: [https://www.youtube.com/watch?v=UfThVvBWZxM&t=19m33s the video @ 19m33s]
 
Open questions:
 
* Why a parallelogram?
* How to properly overlay the parallelogram onto the 3d manifold, in order to do the parallel transport?
* How does this relate to the length computation above?
 


===== Putting it all together =====
===== Putting it all together =====
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