三维Minkowski空间中的特殊曲线和可展曲面  

Special space curve and developable surfaces in Minkowski 3-space

作　　者：王志刚[1] 吕永震[2] 裴东河[3] 樊晓明[1] 罗振江[1] 

机构地区：[1]哈尔滨师范大学呼兰学院数学系,黑龙江哈尔滨150500 [2]北华大学教务处,吉林吉林132013 [3]东北师范大学数学与统计学院,吉林长春130024

出　　处：《东北师大学报（自然科学版）》2008年第2期1-6,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10471020);教育部新世纪杰出人才资助项目(NCET05-0319);黑龙江省教育厅科技项目(11531458)

摘　　要：定义了三维Minkowski空间中一般螺线、斜螺线和锥面测地线,研究了Minkowski一般螺线的等价条件,给出Minkowski斜螺线和锥面测地线作为三维Minkowski空间中的特殊曲线所特有的性质,构造出三维Minkowski空间中的三类可展曲面;研究了Minkowski斜螺线和锥面测地线这两种特殊曲线和这些曲面的关系;还研究了Minkowski斜螺线和锥面测地线作为测地线的一类可展曲面的奇点分类.In this paper, the definitions of Minkowski general helix, Minkowski slant helices and Minkowski conical geodesic curves in Minkowski 3-space are given, equivalence conditions of Minkowski general helix are studied. Three kinds of developable surfaces are construct and the relationship with Minkowski slant helices and Minkowski conical geodesic curves has been studied. By applying the singularity theoerical knowledge, classification of special developable surfaces under the condition of the existence of such a special curve as geodesic was solved.

关 键 词：达布向量 可展曲面 奇点 

分 类 号：O19[理学—数学]