二维流形公理化的早期尝试与应用——《黎曼面的概念》中的流形与黎曼面  

Early attempts and applications of axiomatic two-dimensional manifold:The concept of manifold and Riemann surface in Die Idee der Riemannschen Flche

作　　者：王涛[1,2] 邓明立[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050024 [2]南方科技大学数学系,深圳518055

出　　处：《自然科学史研究》2015年第4期502-514,共13页Studies in The History of Natural Sciences

基　　金：国家自然科学基金(项目编号:11271108;11401161)

摘　　要：《黎曼面的概念》是一部关于复函数论的专著,其中首次给出了二维流形的公理化定义,并以此定义了黎曼面的概念,在流形的发展史上具有重要意义。在掌握原始文献的基础上,介绍了专著的主要内容、特色与影响;分析了外尔引入流形的目的、动机与方法;总结了外尔引入流形的路线;探讨了克莱因、希尔伯特等人对外尔的影响;明晰了外尔1913年对流形与黎曼面概念的贡献,并简要论及了其中反映的数学哲学思想。Die Idee der Riemannschen Fl？che by Hermann Weyl is a monograph on complex theory,which gives the axiomatic definition of two-dimensional manifold for the first time,then defines the concept of Riemann surface. This work is of great significance in the history of the manifold concept. Based on primary sources,the paper introduces the main contents,features and influences of this monograph,and analyses Weyl’s purpose,motivation and means of introducing the concept of manifold. It also sums up the route of Weyl’s introduction of manifold,explores the influence of Klein,Hilbert and others on Weyl,clarifies Weyl’s contribution to the concepts of manifold and Riemann surface in 1913 from an historical perspective,and briefly discusses his mathematical philosophy.

关 键 词：外尔 流形 黎曼面 

分 类 号：O174.5[理学—数学]