CAJ | 학술논문

讨论三维 Minkowski空间中的平移曲面。曲面的性质主要取决于高斯曲率和平均曲率，所以研究曲面的高斯曲率和平均曲率之间的关系，也就是曲面的 Weingarten型有着重要的意义。在三维 Minkowski空间中，存在类空、类时、和类光3种向量，选取这3种向量中的任意2种作为2个平移方向，可以将平移曲面分为6类。在伪正交标架下，选取一种新的度量形式，对沿类光和类空方向平移的平移 Weingarten曲面进行了研究。首先，根据微分几何中的基本知识，得到了该种度量形式下的平移曲面的第1、第2基本形式以及高斯曲率和平均曲率；然后，主要利用高斯曲率和平均曲率之间的线性关系和平方关系，得到了这类平移曲面的分类定理。
토론삼유 Minkowski공간중적평이곡면。곡면적성질주요취결우고사곡솔화평균곡솔，소이연구곡면적고사곡솔화평균곡솔지간적관계，야취시곡면적 Weingarten형유착중요적의의。재삼유 Minkowski공간중，존재류공、류시、화류광3충향량，선취저3충향량중적임의2충작위2개평이방향，가이장평이곡면분위6류。재위정교표가하，선취일충신적도량형식，대연류광화류공방향평이적평이 Weingarten곡면진행료연구。수선，근거미분궤하중적기본지식，득도료해충도량형식하적평이곡면적제1、제2기본형식이급고사곡솔화평균곡솔；연후，주요이용고사곡솔화평균곡솔지간적선성관계화평방관계，득도료저류평이곡면적분류정리。
This paper considers translation surfaces in 3-D Minkowski space.The nature of surface mainly depends on Gaussian curvature and mean curvature,and therefore,it is of significance to investigate the relation between Gaussian curvature and mean curvature of surface,i.e.,Weingarten surface.There are three kinds of vectors in the 3-D Minkowski space,i.e.,space-like,time-like and light-like vectors among which choosing any two vectors as the directions of translation will divide the translation surfaces into six types.A new metric form is chosen to study the Weingarten translation surfaces which are translating in the lightlike direction and spacelike direction in a pseudo-orthogonal frame.Then,the first and second fundamental forms,Gaussian curvature and mean curvature of the surfaces are directly calculated according to the principles of differential geometry.It follows that some theorems of classification of those translation surfaces are given mainly by virtue of the linear and square relationships between the Gaussian curvature and the mean curvature.