微分几何背景下Dini曲面的几何性质研究

Research on the Geometric Properties of the Dini Surface under the Background of Differential Geometry

曲面是经典微分几何研究的主要对象,它的性质很丰富.本文以Dini曲面为背景,以微分几何为工具,讨论了三维欧氏空间中Dini曲面的有关几何性质,给出了Dini曲面的主曲率、高斯曲率、平均曲率等几何性质;再由高斯曲率、平均曲率,得到Dini曲面的极小轨迹。

Surface is main object of the classic differential geometry, which has a lot of differential geometry, Based on the Dini surface as the background, Dini in three dimensional Euclidean space were discussed about the geometric properties of the surface. Gives the Dini surface asymptote, main curvature , gaussian curvature and mean curvature geometry properties; Again by gaussian curvature and mean curvature, obtained the Dini tiny trajectory of the surface.