Finsler connection in moving frame formalism

2018/11/30 by Ootsuka, Takayoshi, Ishida, Muneyuki, Yahagi, Ryoko
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1811.12716

Abstract

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) θ^a=e^a_μdx^μ 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^μ, but only on moving frame θ^a: L=L(θ).

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