math214:hw10
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math214:hw10 [2020/04/04 09:52] pzhou |
math214:hw10 [2020/04/12 09:44] (current) pzhou [Problem 4] |
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| $$ A = x dy - y d x $$ | $$ A = x dy - y d x $$ | ||
| Let point $a=(1,0)$, $b=(-1,0)$, and $\gamma_\pm$ be path from $a$ to $b$, going along upper (or lower) semicircle: | Let point $a=(1,0)$, $b=(-1,0)$, and $\gamma_\pm$ be path from $a$ to $b$, going along upper (or lower) semicircle: | ||
| - | $$ \gamma_\pm: [0,1] \to \R^2, \quad t \mapsto (\cos t, \pm \sin t). $$ | + | $$ \gamma_\pm: [0,\pi] \to \R^2, \quad t \mapsto (\cos t, \pm \sin t). $$ |
| Question: compute the parallel transport along $\gamma_+$ and $\gamma_-$. | Question: compute the parallel transport along $\gamma_+$ and $\gamma_-$. | ||
math214/hw10.1586019154.txt.gz · Last modified: 2020/04/04 09:52 by pzhou
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