| 微分流形及其应用的某些注释 |
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| 引用本文： | 赵培标.微分流形及其应用的某些注释[J].周口师范学院学报,2007,24(2):4-10. |
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| 作者姓名： | 赵培标 |
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| 作者单位： | 南京理工大学,应用数学系,南京,210094 |
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| 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.
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| 关 键 词： | 黎曼流形 次黎曼流形 方向导数 共变导数 联络 |
| 文章编号： | 1671-9476（2007）02-0004-07 |
| 收稿时间： | 2006-10-12 |
| 修稿时间： | 2006年10月12 |
Some remarks on differential manifolds and their applications |
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| ZHAO Pei-biao.Some remarks on differential manifolds and their applications[J].Journal of Zhoukou Normal University,2007,24(2):4-10. |
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| Authors: | ZHAO Pei-biao |
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| Abstract: | 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. |
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| Keywords: | Riemannian manifolds sub- Riemannian manifolds directional derivatives covariant derivatives connection |
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