It is still a long-standing open problem in Finsler geometry, is there any regular Landsberg metric which is not Berwaldian. However, there are non-regular Landsberg metrics which are not Berwladian. The known examples are established by G. S. Asanov and Z. Shen. In this paper, we use the Maple program to study some explicit examples of non-Berwaldian Landsberg metrics. In fact, such kinds of examples are very tedious and complicated to investigate. Nonetheless, we use the maple program and Finsler packages to simplify the calculations in an elegant way. Depending on these examples, we manage to figure out some geometric properties of the geodesic spray of a non-Berwaldain Landsberg metric. Deforming this spray in a very specific way, using the metrizability tools of the deformed spray, we get new (very simple) non-Berwaldian Landsberg metrics. Moreover, the powerful of this procedure is investigating a very simple and useful formula for the general class obtained by Z. Shen.

中文翻译：

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Finsler 几何中 Landsberg 独角兽问题的解

Finsler 几何中仍然是一个长期悬而未决的问题，是否有任何不是 Berwaldian 的常规 Landsberg 度量。但是，有一些非常规的 Landsberg 度量不是 Berwladian。已知的例子是由 GS Asanov 和 Z. Shen 建立的。在本文中，我们使用 Maple 程序来研究非 Berwaldian Landsberg 度量的一些显式示例。实际上，此类示例非常繁琐且研究起来很复杂。尽管如此，我们还是使用 maple 程序和 Finsler 包以优雅的方式简化计算。根据这些示例，我们设法找出非 Berwaldain Landsberg 度量的测地线喷雾的一些几何属性。以非常具体的方式使这种喷雾变形，使用变形喷雾的度量工具，我们得到新的（非常简单的）非 Berwaldian Landsberg 度量。