低维欧式空间中的一般管问题

Generalized tubes in low-dimensional space

讨论了围绕三维欧式空间中曲线、曲面的一般性管问题,利用古典微分几何方法在低维空间中得到具有连续变化半径的管体积一般公式以及围绕曲线和曲面的管内具有对称横截区域体积的积分表示,对管体积公式作了进一步推广。

The paper discusses the generalized tubes around curved lines and surfaces in three-dimensional space. By using classical differential geometry in low-dimensional space, the formula of volumn of tubes with changing radius and that of regions with symmetric cross section in the tubes around curved line and surface are gained. These formulae of tube vulumn are then further extended.