math214:hw11
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math214:hw11 [2020/04/10 16:44] pzhou |
math214:hw11 [2020/04/15 10:47] (current) pzhou |
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| $$ (0, 2\pi] \times (-\delta, \delta) \to \R^3$$ | $$ (0, 2\pi] \times (-\delta, \delta) \to \R^3$$ | ||
| where | where | ||
| - | $$ (\phi, z) \mapsto ((1 + z \sin (\phi/2) ) \cos \phi, (1 + z \cos (\phi/2) ) \sin \phi, z \cos(\phi/ | + | $$ (\phi, z) \mapsto ((1 + z \sin (\phi/2) ) \cos \phi, (1 + z \sin (\phi/2) ) \sin \phi, z \cos(\phi/ |
| Question: is the induced metric on $M$ flat? | Question: is the induced metric on $M$ flat? | ||
| + | |||
| + | {{ : | ||
| 3. (Wiggly band): Let $M$ be a submanifold of $\R^3$ defined by the following embedding | 3. (Wiggly band): Let $M$ be a submanifold of $\R^3$ defined by the following embedding | ||
math214/hw11.1586562272.txt.gz · Last modified: 2020/04/10 16:44 by pzhou
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