Question: Let be a curve on a surface M. The geodesic curvature of , denoted by kg(), is given by kg() = 00(t).( 0 (t) U)

Let be a curve on a surface M. The geodesic curvature of , denoted by kg(), is given by kg() = 00(t).( 0 (t) U) where U is the unit normal vectore eld to M. Show that || 00(t)||2 = kg() 2 + k( 0 (t)) where k( 0 (t)) is the normal curvature in the direction of 0 .

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