So this other day I found the problem stated below... And I just can't solve the bloody thing. So, any help is more than welcome. The only thing I know is that Clairaut's thm is to be used... however I don't see how.
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The regular surface S in R^3 is parametrised by
X(u,v) = (cosv(2+cosu),sinv(2+cosu),sinu)
let g = (x,y,z) be the geodesic on S satisying
g(0) = (3,0,0) and g'(0) = (0,1/sqrt(2),1/sqrt(2))
Determine the value inf(x^2(s) + y^2(s)).
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Yes, it has been i while sice I actually picked up a Diff. Geo. book so be very explicit.