Finsler connection in moving frame formalism

In our previous work, we have defined a nonlinear connection of Finsler manifold which preserves the Finsler metric $L=L(x,dx)$. To make the method easier and more useful in applications, moving frame (vielbein) $\theta^a={e^a}_\mu dx^\mu$ formalism for the nonlinear connection is newly considered. We derive formulae to calculate the Finsler connection in the specific case that the Finsler metric depends not on coordinates $x^\mu$, but only on moving frame $\theta^a$: $L=L(\theta)$.