论文标题
Finsler指标的第一个积分，其消失$χ$ curvature
First integrals for Finsler metrics with vanishing $χ$-curvature
论文作者
论文摘要
我们证明，在消失的$χ$ curvature（尤其是恒定标志曲率）中，某些非河流几何结构是地球上不变的，因此它们诱导一组非Riemannian的第一个积分。这些第一积分的替代表达式可以根据平均Berwald曲率或平均Cartan扭转和平均Landsberg曲率的功能获得。
We prove that in a Finsler manifold with vanishing $χ$-curvature (in particular with constant flag curvature) some non-Riemannian geometric structures are geodesically invariant and hence they induce a set of non-Riemannian first integrals. Two alternative expressions of these first integrals can be obtained either in terms of the mean Berwald curvature, or as functions of the mean Cartan torsion and the mean Landsberg curvature.
