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

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.