《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (8): 13-20.doi: 10.6040/j.issn.1671-9352.0.2023.453
• • 上一篇
曲瑞祥,田涵宇,于延华*
QU Ruixiang, TIAN Hanyu, YU Yanhua*
摘要： 在四维欧氏空间中,利用腰曲线的定义,提出直纹面的结构函数,将三维欧氏空间中的不可展直纹面及其标准方程推广到四维欧氏空间。通过直纹面的结构函数来研究曲面自身的性质,得到4类特殊伴随直纹面的结构函数、导线和腰曲线之间的关系,并对这些直纹面进行分类。最后给出导线是Mannheim曲线和第三型斜角螺线时结构函数的具体表达式,并计算此时伴随直纹面的平均曲率向量场。
中图分类号:
| [1] RAVANI B, WANG J W.Computer aided geometric design of line constructs[J]. Journal of Mechanical Design, 1991, 113(4):363-371. [2] HOSCHEK J. Eine verallgemeinerung des satzes von holditch[J]. Monatshefte Für Mathematik, 1975, 80(2):93-99. [3] POTTMANN H, WALLNER J. Computational line geometry[J]. Journal of Theoretical Biology, 2001, 86(507):207-223. [4] ELBER G, FISH R. 5-axis freeform surface milling using piecewise ruled surface approximation[J]. Journal of Manufacturing Science & Engineering, 1997, 119:383-387. [5] LIU H L, YU Y H, JUNG S D. Invariants of non-developable ruled surfaces in Euclidean 3-space[J]. Beitrage zur Algebra und Geometrie, 2014, 55(1):189-199. [6] YU Y H, YANG Y, LIU H L. Centroaffine ruled surfaces in R3[J]. Journal of Mathematical Analysis and Applications, 2010, 365(2):683-693. [7] LIU H L. Characterizations of ruled surfaces with lightlike ruling in minkowski 3-space[J]. Results in Mathematics, 2009, 56(1):357. [8] SAJI K. Singularities of non-degenerate 2-ruled hypersurfaces in 4-space[J]. Hiroshima Mathematical Journal, 2002, 32:309-323. [9] ALTIN M, KAZAN A, YOON D W. 2-ruled hypersurfaces in Euclidean 4-space[J]. Journal of Geometry and Physics, 2021, 166:104236. [10] MATSUD H, YOROZU S. On generalized Mannheim curves in Euclidean 4-space[J]. Nihonkai Mathematical Journal, 2009, 20(1):33-56. [11] ALI A, TURGU M. Some characterizations of slant helices in the Euclidean space En[J]. Hacettepe Journal of Mathematics and Statistics, 2010, 39:327-336. |
| [1] | 毕晓冬 . 完全正则半群的一个构造方法[J]. J4, 2007, 42(1): 40-43 . |
|
||
