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Solutions for the Landsberg unicorn problem in Finsler geometry

Journal of Geometry and Physics • 2020
العودة
معلومات البحث
المؤلفون Salah Elgendi
الكلمات المفتاحية Berwald metrics; Landsberg metrics; (α; β)-metrics, Finsler packages; Maple program
المجلة العلمية Journal of Geometry and Physics
الناشر ScienceDirect
المجلد Not Available
العدد Not Available
الصفحات Not Available
publication.type International
رابط البحث Open Link
المواد المرفقة Not Available
الملخص
t is still a long-standing open problem in Finsler geometry, is there any regularLandsberg metric which is not Berwaldian. However, there are non-regular Landsbergmetrics which are not Berwaldian. The known examples are established by G. S. Asanovand Z. Shen. In this paper, we use the Maple program to study some explicit examplesof non-Berwaldian Landsberg metrics. In fact, such kinds of examples are very tediousand complicated to investigate. Nonetheless, we use the Maple program and Finslerpackages to simplify calculations. Depending on these examples, we manage to figureout some geometric properties of the geodesic spray of a non-Berwaldian Landsbergmetric. Deforming this spray in a very specific way, using the metrizability tools of the deformed spray, we get new(very simple)non-BerwaldianLandsbergmetrics.Moreover, the power of this procedure consists in investigating a simple and useful formula for the general class obtained by Z. She