一类光滑曲面的保面积投影  

The area-preserving projection of some smooth surfaces

作　　者：王宝勤[1] 周小辉[2] 王刚[1] 

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830054 [2]石河子大学理学院,新疆石河子832061

出　　处：《西北大学学报（自然科学版）》2012年第6期877-881,共5页Journal of Northwest University（Natural Science Edition）

基　　金：新疆维吾尔自治区高校科研计划青年教师培育基金资助项目(XJEDU2009S67)

摘　　要：目的提出一类光滑曲面的一种切实可行的构造保面积映射的方法。方法先构造了单位球面上的保面积投影,再把它与高斯映射结合组成复合的保面积投影。结果可以做对非零常高斯曲率光滑曲面在平面上的保面积投影,并给出了两个例子。结论给出的保面积投影方法为进一步构造某些光滑二维流形M的L2(M)上的多分辨分析和M上的小波变换奠定了基础。Aim A method for constructing a feasible area-preserving projection on some smooth surfaces is presen- ted and found in this paper. Methods Firstly, the area-preserving projection on the unit sphere is constructed. Then combining it with Gauss mapping forms a composite area-preserving projection. Results It can be done that constructing the area-preserving projection from smooth surfaces with non-zero constant Gauss curvature to a plane, and two examples are given. Conclusion The method of an area-preserving projection is given in this paper for constructing a multi-resolution analysis on the L2 （M） of some smooth manifolds M, laying a foundation of the wave- let transform on M.

关 键 词：高斯映射 保面积投影 光滑曲面 

分 类 号：O189.16[理学—数学]