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Results tagged with torsion
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user 14454
0
votes
1
answer
379
views
Torsion and submanifolds [closed]
EDIT: Let me modify the question then: for what submanifolds $N$ does the torsion $T$ preserve tangent vectors to $N$? … If $\nabla$ is a connection on a manifold $M$, then torsion is defined to be the map
$$
T(X,Y)=\nabla_XY-\nabla_YX-[X,Y]
$$
where $X$ and $Y$ are vector fields on $M$. …
- 1,378
21
votes
2
answers
5k
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Torsion and parallel transport
It seems to me that there should be an analogous result for torsion. I believe that torsion measures the extent to which certain geodesic parallelograms don't close. …
- 1,378