On Main Scalar of Two Dimentional Finsler Spaces with (α, β) - Metrics

摘要

In this paper, we prove a formula to calculation main scalar I in two dimentional Finsler spaces equipped with (α,β) - metrics. Then based on the obtained results, we obtain main scalar of a two dimentional Finsler space equipped with general (α,β) - metric F = α + κβ + εβ~2/α (where k and ε are constants and k ≠ ε = 0) and some special cases like F = α + β + β~2/α (the first approximate Matsumoto metric), F = (α + β)~2/α (square metric).