Finsler Geometry

For each point x of M, and for every vector v in the tangent space T_xM, the second derivative of the function L:T_xM->R given by

$L(\backslash bold\{w\})=\backslash frac\{1\}\{2\}\backslash |w\backslash |^2$

at v is positive definite.

$\backslash int\; \backslash left\backslash |\backslash frac\{d\backslash gamma\}\{dt\}(t)\backslash right\backslash |\; dt$.

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