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| R13中混合型曲面保主曲率等距变形 | |
| 引用本文： | 王小平,周儒荣,叶正麟. R13中混合型曲面保主曲率等距变形[J]. 数学研究及应用, 2003, 23(2): 287-293 |
| 作者姓名： | 王小平 周儒荣 叶正麟 |
| 作者单位： | 南京航空航天大学CAD/CAM工程研究中心,江苏,南京,210016;南京航空航天大学CAD/CAM工程研究中心,江苏,南京,210016;西北工业大学数学与信息科学系,陕西,西安,710072 |
| 摘 要： | 本文研究了Minkowski空间R13曲面的等距变形问题.建立了R13中曲面的共形、等距等概念.推广了O.Bonnet和S.S.Chern关于欧氏空间的结论.对R13出现的新情况——曲面的中曲率梯度类光作了一定探讨,得出的主要结果为:非平坦的、允许保主曲率等距变形的曲面一定不是W-曲面. |
| 关 键 词： | 等距变形 中曲率 W-曲面 |
| 文章编号： | 1000-341X(2003)02-0287-07 |
| 收稿时间： | 2000-07-18 |
| 修稿时间： | 2000-07-18 |
Deformation Preserving Principal Curvatrue of Surfaces in R13 |
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| WANG Xiao-ping,ZHOU Ru-rong and YE Zheng-lin. Deformation Preserving Principal Curvatrue of Surfaces in R13[J]. Journal of Mathematical Research with Applications, 2003, 23(2): 287-293 | |
| Authors: | WANG Xiao-ping ZHOU Ru-rong YE Zheng-lin |
| Affiliation: | Research Center of CAD/CAM Engineering; Nanjing Univ. of Aeronautics and Astronautics; Jiangsu; China;Research Center of CAD/CAM Engineering; Nanjing Univ. of Aeronautics and Astronautics; Jiangsu; China;Dept. of Math. &. Info. Sci.; Northwestern Polytechnical Univ.; Xi'an; China |
| Abstract: | In this paper, we mainly study the isometric deformation preserving principal curvature of surfaces in Minkowski space R13. By generalizing some concepts from R3 to R13, we find these conclusions drawn by O. Bonnet or S. S. Chern are still hold in R13. Moreover, we research the new case that the gradient of mean curvature is null and get some meaningful results , of which main conclusion is that non-flat surfaces that can be isometrically deformed preserving the principal curvature is certainly not W-surface. |
| Keywords: | isometric deformation mean curvature W-surface |
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