Curve Length

Let gamma(t) be a smooth curve in a manifold M from x to y with gamma(0)=x and gamma(1)=y. Then gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x. The length of gamma with respect to the Riemannian structure is given by

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Weisstein, Eric W. "Curve Length." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CurveLength.html

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