If $f:[0,1]\rightarrow \mathbb{R}^d$ is a smooth curve, then is there are relationship between the total variation of $f$ and the geodesic curvature of $f$?
I expect they both should be zero iff $f$ is a line but how to make this clear?
2026-03-28 12:13:20.1774700000
Total Variation and geodesic Curvature
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