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## Main Question or Discussion Point

If [itex]f:[a,b] \to R[/itex] is a positive real function and[itex]\gamma(u,v) = ( f(u)\cos (v), f(u) \sin (v), u)[/itex] then show that

[itex]\gamma(t) = \sigma(u(t), c)[/itex] is a geodesic in [itex]M[/itex]where [itex]c[/itex] is a constant between 0 and[itex]2\pi[/itex] and

[itex]M=\sigma(U)[/itex] where [itex]U= \{ (u,v)| a<u<b and 0<v< 2\pi \}[/itex]

Actually , I tried to calculate the second derivative of

[itex]\sigma(t)[/itex] but that did not work and also I still have u in the first derivative

which means it is not constant

any suggestion? :\

Thanx

[itex]\gamma(t) = \sigma(u(t), c)[/itex] is a geodesic in [itex]M[/itex]where [itex]c[/itex] is a constant between 0 and[itex]2\pi[/itex] and

[itex]M=\sigma(U)[/itex] where [itex]U= \{ (u,v)| a<u<b and 0<v< 2\pi \}[/itex]

Actually , I tried to calculate the second derivative of

[itex]\sigma(t)[/itex] but that did not work and also I still have u in the first derivative

which means it is not constant

any suggestion? :\

Thanx