黎曼流形上关于曲线管体积的完全公式  

Complete Formulas of the Volumes for Tubes about Curves in a Reimannian Manifold

作　　者：吴发恩[1] 

机构地区：[1]北方交通大学数学系,北京100044

出　　处：《数学学报（中文版）》2003年第2期321-324,共4页Acta Mathematica Sinica：Chinese Series

摘　　要：利用Jacobi场方程解的Taylor展开式,得到了黎曼流形上关于曲线管体积 相对于管半径的幂级数展开的完全公式.这简化、推广和统一了已有结果.By using of the Taylor expansions of the solutions of Jacobi equations, we obtain the complete formulas for the volumes of tubes about curves in a Riemannian manifold. This unifies the known results and simplifies the compulations involved in this direction. In the special case of surfaces, we also obtain the corresponding complete formula which generalize the known results.

关 键 词：黎曼流形 曲线管体积 完全公式 Fermi坐标 N-Jacobi场 

分 类 号：O186.12[理学—数学]