The Differential Geometry of Finsler Spaces
The Differential Geometry of Finsler Spaces
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DOI：
10.1007/978-3-642-51610-8
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发表时间：
1959
期刊：
影响因子：
--
通讯作者：
H. Rund
中科院分区：
文献类型：
--
作者：
H. Rund
这本专著有两个截然不同的目的。首先，在经典微分几何方法的基础上，对Finsler空间的理论进行了较为全面的阐述。其次，人们希望这本专著也可以作为微分几何的一个分支的介绍，该分支与理论物理中的各种主题密切相关，特别是分析动力学和几何光学。考虑到第二个目标，人们试图更详细地描述该理论的基本方面--即使是以简明性为代价--而在后面几章的更专业的部分，可能主要是专家感兴趣的部分，则采用了更简洁的风格。关于芬斯勒几何学存在着几种根本不同的观点，这一事实使得写一份连贯的报告变得相当困难。这句话不仅与该学科在张量演算基础上的发展有关，而且在更广泛的意义上也适用。H.Busemann的广泛工作开辟了独立于经典张量分析方法的Finsler几何的新途径。因此，在后一种意义上，对这种方法的全面描述不属于本论文的范围，尽管其根本的L意义是毋庸置疑的。
The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail-even at the expense of conciseness-while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted.