math121b:sample-m1
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math121b:sample-m1 [2020/02/22 18:08] pzhou [Partial Solution] |
math121b:sample-m1 [2020/02/23 16:56] (current) pzhou |
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| The divergence of $V$ is | The divergence of $V$ is | ||
| - | $$ div(V) = H^{-2} \d_u (H^2) = 2 \cosh(u)/\sinh(u) $$ | + | $$ div(V) = H^{-2} \d_u (H^2) = \frac{2 \cosh(u)\sinh(u)}{ \sinh^2(u) + \sin^2(v) }$$ |
| More details: $V = 1 \d_u + 0 \d_v$ so $V^1 = 1$, $V^2=0$, and $\sqrt{g} = \sqrt{H^4} = H^2$. Plug in the divergence formula will yield the answer. | More details: $V = 1 \d_u + 0 \d_v$ so $V^1 = 1$, $V^2=0$, and $\sqrt{g} = \sqrt{H^4} = H^2$. Plug in the divergence formula will yield the answer. | ||
math121b/sample-m1.1582423736.txt.gz · Last modified: 2020/02/22 18:08 by pzhou
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