Visualizing a Parallel Field in a Curved Manifold - Maple Application Center
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Visualizing a Parallel Field in a Curved Manifold

: Maplesoft AuthorDr. Robert Lopez
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My PhD thesis was in relativistic cosmology, a study that took me into differential geometry, continuous group theory, and tensor calculus. One of the most difficult concepts in all this was the notion of parallel transport of a vector from one tangent space to another. Of course, the image I had in my head was a basketball for a manifold, and a vector in a tangent plane on this (unit) sphere. The manifold sat in an enveloping R3, and I struggled mightily to visualize the difference between the transported field appearing parallel to the surface observer and Euclidean parallelism as seen by an external observer. The Kantian imperative is true - it's natural to imagine the vectors in R3, but devilishly difficult to visualize the difference between Euclidean parallelism and parallel transport in an intrinsically curved space.

Application Details

Publish Date: January 28, 2010
Created In: Maple 13
Language: English

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