Length of a curve

In a pseudo-Riemannian manifold $(M,g)$ we define the length of a curve $c:[0,1]\to M$ by

$$ l(c):=\int_0^1 \sqrt{g(c'(t),c'(t))}dt $$

Related: energy of a curve.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es


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