楚雄师范学院学报
楚雄師範學院學報
초웅사범학원학보
JOURNAL OF CHUXIONG TEACHERS'COLLEGE
2015年
3期
1-5
,共5页
副法线曲面%高斯曲率%极小轨迹%主曲率
副法線麯麵%高斯麯率%極小軌跡%主麯率
부법선곡면%고사곡솔%겁소궤적%주곡솔
binormal surfaces%Gaussian curvature%minimal locus%principal curvature
通过类比一般空间曲线、曲面的研究方法，讨论了三维欧氏空间中曲线的副法线曲面，给出了副法线曲面的渐近线和曲率线；再由高斯曲率、平均曲率，得到了副法线曲面上常高斯曲率曲线、极小轨迹；最后，利用高斯曲率和平均曲率之间的线性关系和平方关系，得到了副法线曲面的分类定理。
通過類比一般空間麯線、麯麵的研究方法，討論瞭三維歐氏空間中麯線的副法線麯麵，給齣瞭副法線麯麵的漸近線和麯率線；再由高斯麯率、平均麯率，得到瞭副法線麯麵上常高斯麯率麯線、極小軌跡；最後，利用高斯麯率和平均麯率之間的線性關繫和平方關繫，得到瞭副法線麯麵的分類定理。
통과류비일반공간곡선、곡면적연구방법，토론료삼유구씨공간중곡선적부법선곡면，급출료부법선곡면적점근선화곡솔선；재유고사곡솔、평균곡솔，득도료부법선곡면상상고사곡솔곡선、겁소궤적；최후，이용고사곡솔화평균곡솔지간적선성관계화평방관계，득도료부법선곡면적분류정리。
By analogy to the research methods on the general space curves and surfaces,We discussed the binormal surfaces,and get the asymptotic curves and curvature . Then,based on the Gaussian curva-ture and the mean curvature,the curves with constant Gaussian curvature and minimal locus are obtained. It follows that some theorems of classification of those binormal surfaces are given by virtue of the linear and square relationships between the Gaussian curvature and the mean curvature.
