Geodesic torsion

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let a(t) be a regular curve which lies on the unit sphere in R^3

a(t) . a(t) = 1 for all t

i want to show that the geodesic torsion Tg(t) vanishes for such a curve.

i can use the fact that a(t) can be interpreted as a unit normal N(t) to the surface along he curve.

can anyone help me with this question? thanks

my solution:

i couldnt understand how Tg(t) torsion is related to this question. I didnt know how to relate it to it

but i was thinking if a(t) is a regular curve then its Xu x Xv /= 0. and unit normal would be Xu x Xv / ||Xu x Xv|| , bot i cant understand how i would relate this to geodesic torsion?

any help?
 

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