First integrals for Finsler metrics with vanishing $\chi $-curvature

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2022-09-02 DOI:10.1007/s10455-022-09872-y

Ioan Bucataru, Oana Constantinescu, Georgeta Creţu

引用次数: 0

Abstract

We prove that in a Finsler manifold with vanishing $\chi $-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.

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具有消失$$\chi$$-曲率的Finsler度量的第一积分

我们证明了在具有消失曲率（特别是具有常旗曲率）的Finsler流形中，一些非黎曼几何结构是测地不变的，因此它们导出了一组非黎曼第一积分。这些第一积分的两个替代表达式可以根据平均Berwald曲率获得，也可以作为平均Cartan扭转和平均Landsberg曲率的函数获得。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.

First integrals for Finsler metrics with vanishing \(\chi \)-curvature

Abstract