高斯-博内-陈定理的历史发展及其意义  

The Historical Development and the Meaning of Gauss-Bonnet-Chern Theorem

作　　者：陈惠勇[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2011年第1期106-110,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10071085)资助项目

摘　　要：高斯-博内定理是大范围微分几何学的一个经典定理,它建立了黎曼流形的局部性质和整体性质之间的联系,因而被认为是曲面微分几何学中最深刻的定理.通过考察高斯-博内-陈定理的历史发展,指出高斯-博内-陈定理在黎曼流形、微分流形以及拓扑流形上的表现形式,以此阐明高斯-博内-陈定理与现代数学的深刻联系及其意义.Gauss-Bonnet theorem,which established a link between the local nature of Riemannian manifold and the overall’s,is a classic theorem of differential geometry in the large,and considered to be the most profound theorem in differential geometry.The historical development of the Gauss-Bonnet-Chern theorem are examined,the manifestations of the Gauss-Bonnet-Chern theorem in Riemannian manifolds,differential manifolds,and topology manifolds are dis-cussed,and the deep relations and meaning between the Gauss-Bonnet-Chern theorem and the modern mathematics are clarified as well.

关 键 词：高斯 高斯-博内-陈定理 整体微分几何 

分 类 号：O186.1[理学—数学]