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题名/责任者:

Lectures on Finsler geometry / Zhongmin Shen.

出版发行项:

Singapore ; River Edge, NJ : World Scientific, 2001.

ISBN:

9789810245313 :

载体形态项:

xiv, 307 pages : illustrations ; 23 cm

个人责任者:

Shen, Zhongmin, 1963- author.

论题主题:

Finsler spaces.

论题主题:

Geometry, Differential.

中图法分类号:

O186.14

书目附注:

Includes bibliographical references (pages 299-304) and index.

摘要附注:

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 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.

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