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## Homework Statement

What curves lying on a sphere have constant geodesic curvature?

## Homework Equations

k^2 = (k_g)^2 + (K_n)^2

## The Attempt at a Solution

I'm trying to understand the solution given in the back of the book. It says, a curve on a sphere will have constant curvature. But, is it true that every curve on a sphere has constant normal curvature? The definition of normal curvature I'm using is "the length of the projection of the vector kn over the normal to the surface at p."