Developable surfaces in Euclidean space

被引：14
|
作者：
Ushakov, V [1 ]
机构：
[1] Univ Melbourne, Dept Math, Parkville, Vic 3052, Australia
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS | 1999年 / 66卷
关键词：
developable surface; planar point; ruled surface; flat metric; point codimension of a surface; local codimension of a surface; affinely stable immersion;
D O I：
10.1017/S1446788700036685
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The classical notion of a two-dimensional developable surface in Euclidean three-space is extended to the case of arbitrary dimension and codimension. A collection of characteristic properties is presented. The theorems are stated with the minimal possible integer smoothness. The main tool of the investigation is Cartan's moving frame method.
引用
收藏
页码：388 / 402
页数：15
相关论文
共 50 条
  • [21] Stationary rotating surfaces in Euclidean space
    Rafael López
    Calculus of Variations and Partial Differential Equations, 2010, 39 : 333 - 359
  • [22] Stationary rotating surfaces in Euclidean space
    Lopez, Rafael
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 39 (3-4) : 333 - 359
  • [23] Surfaces of Revolution of Frontals in the Euclidean Space
    Masatomo Takahashi
    Keisuke Teramoto
    Bulletin of the Brazilian Mathematical Society, New Series, 2020, 51 : 887 - 914
  • [24] Surfaces of Osculating Circles in Euclidean Space
    Rafael López
    Çetin Camci
    Ali Uçum
    Kazim Ilarslan
    Vietnam Journal of Mathematics, 2024, 52 : 197 - 210
  • [25] Singularities for Timelike Developable Surfaces in Minkowski 3-Space
    Li, Yanlin
    Chen, Zhizhi
    Nazra, Sahar H. H.
    Abdel-Baky, Rashad A. A.
    SYMMETRY-BASEL, 2023, 15 (02):
  • [26] The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space
    Li, Yanlin
    Eren, Kemal
    Ayvaci, Kebire Hilal
    Ersoy, Soley
    AIMS MATHEMATICS, 2023, 8 (01): : 2226 - 2239
  • [27] PARALLEL SURFACES TO TRANSLATION SURFACES IN EUCLIDEAN 3-SPACE
    Cetin, Muhammed
    Tuncer, Yilmaz
    COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2015, 64 (02): : 47 - 54
  • [28] Minimal surfaces with bounded curvature in Euclidean Space
    Soret, M
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2001, 9 (05) : 921 - 950
  • [29] CLAIRAUT SURFACES IN EUCLIDEAN THREE-SPACE
    Hwang, Andrew D.
    Wang, Xinyi
    TOHOKU MATHEMATICAL JOURNAL, 2022, 74 (02) : 215 - 227
  • [30] Constructions of Helicoidal Surfaces in Euclidean Space with Density
    Yoon, Dae Won
    Kim, Dong-Soo
    Kim, Young Ho
    Lee, Jae Won
    SYMMETRY-BASEL, 2017, 9 (09):
12345