Let 
be a smooth curve in a manifold 
from 
to 
with 
and 
. Then 
where 
is the tangent space of
at 
. The length of 
with respect to the Riemannian structure is given by
 |
Curve Length
See also
Arc Length, DistanceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Curve Length." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CurveLength.html