- #1
moo5003
- 202
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I'm reviewing for my final and there is a question I can't seem to solve. If anyone could help me with it I would appreciate it very much.
A ruled surface has the parameterization of the form:
x(s,t) = A(s) + tB(s)
where A(s) is unit speed, |B(s)| = 1.
Show that: K<or= to 0.
So, my first though was to just calculate the g_ij's and then just find its determinant and plug it into the equation:
K = (R_1L21 * g_L2)/g ~ Summed for L = 1,2
But after calculate some of the metric coeff's I'm not sure it will work out all that well. Any help would be appreciated.
' = d/ds
g_12 = g_21 = <A',B>
g_11 = 1 + 2t<A',B'> + t^2<B',B'>
g_22 = 1
A ruled surface has the parameterization of the form:
x(s,t) = A(s) + tB(s)
where A(s) is unit speed, |B(s)| = 1.
Show that: K<or= to 0.
So, my first though was to just calculate the g_ij's and then just find its determinant and plug it into the equation:
K = (R_1L21 * g_L2)/g ~ Summed for L = 1,2
But after calculate some of the metric coeff's I'm not sure it will work out all that well. Any help would be appreciated.
' = d/ds
g_12 = g_21 = <A',B>
g_11 = 1 + 2t<A',B'> + t^2<B',B'>
g_22 = 1