A Kind of Rectilinear Congruences in the Minkowski 3-Space  

三维Minkowski空间中的一类直线汇(英文)

作　　者：侯中华 李丽 

机构地区：[1]Department of Applied Mathematics, Dalian University of Technology [2]College of Stat.& Applied Mathematics, Anhui University of Fin.& Econ.

出　　处：《Journal of Mathematical Research and Exposition》2008年第4期911-918,共8页数学研究与评论（英文版）

基　　金：Specialized Research Fund for the Doctoral Program of Higher Education (No.20050141011)

摘　　要：We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the...We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the net of asymptotic curves. At last, we investigate the orthogonal surface S of T. We proved that the correspondence between S1 and S2 preserves the net of asymptotic curves if S is maximal in E13.

关 键 词：the rectilinear congruence the focal surfaces the Minkowski space the space-like surface maximal surfaces. 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]