Lectures on Finsler Geometry is popular PDF and ePub book, written by Zhongmin Shen in 2001, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lectures on Finsler Geometry can be Read Online from any device for your convenience.
Lectures on Finsler Geometry Book PDF Summary
In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.
Detail Book of Lectures on Finsler Geometry PDF
- Author : Zhongmin Shen
- Release : 01 October 2024
- Publisher : World Scientific
- ISBN : 9810245319
- Genre : Mathematics
- Total Page : 328 pages
- Language : English
- PDF File Size : 18,7 Mb
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