Given a Riemannian manifold \((M,g)\). Then the energy of a curve segment \(\gamma:[a,b]\to M\) is given by
\begin{equation*} E(\gamma)= \frac{1}{2} \int_{a}^{b} \lvert \gamma'(t)\rvert_g^2 dt. \end{equation*}Given a Riemannian manifold \((M,g)\). Then the energy of a curve segment \(\gamma:[a,b]\to M\) is given by
\begin{equation*} E(\gamma)= \frac{1}{2} \int_{a}^{b} \lvert \gamma'(t)\rvert_g^2 dt. \end{equation*}