微分流形及其应用的某些注释(英文)  

Some remarks on differential manifolds and their applications

作　　者：赵培标[1] 

机构地区：[1]南京理工大学应用数学系,南京210094

出　　处：《周口师范学院学报》2007年第2期4-10,共7页Journal of Zhoukou Normal University

基　　金：Supported by a Grant-in-Aid for Scientific Research from Nanjing University of Science and Technology(No.AB96137)a;partially by the National Natural Science Foundation of China(No.10471063)

摘　　要：基于黎曼流形及次黎曼流形在控制论、动力系统、规范场论等领域中的广泛应用的事实,本文拟对作为研究生课程的《微分流形及其应用》给出研习该课程的一般方法和思路.作为一个应用,用微分流形的语式给出Hamilton-Jacobi-Equations表示式.The studies of differential manifolds and their applications are motivated to the active fields with applications of Riemanian manifolds and Sub-Riemannian manifolds in Control Theory, Dynamics Theory, Gauge Fields, etc. We here investigate the ideas and approaches of differential manifolds as a course for postgraduates, and give out the thought of trains with studying this subject. As a conclusion, we also obtain the well known Hamilton-Jacobi-Equations in differential manifold languages.

关 键 词：黎曼流形 次黎曼流形 方向导数 共变导数 联络 

分 类 号：O186.20[理学—数学]