复射影空间CP^(n)(c)中A2型实超曲面上Sasaki磁场下的外在圆轨道

Extrinsic Circular Trajectories under Sasaki Magnetic Fields on Real Hypersurfaces of Type A;in a Complex Projective Space CP^(n)(c)

研究曲面的一种重要方法是利用曲线刻画曲线所在曲面的性质。这里重点考察了复射影空间CP^(n)(c)中A;型实超曲面上Sasaki磁场下的轨道。Sasaki磁场是由实超曲面的构造定义的闭2-形式,Sasaki磁场下的轨道是单位带电粒子在该磁场下的运动轨迹。为了了解运动轨迹通常与一些特殊的简单曲线之间作比较,如测底线、圆等。文中分析了复射影空间CP^(n)(c)中A;型实超曲面上Sasaki磁场下外在圆轨道的外在测地曲率和外在复挠率之间的关系。

An important method to study surfaces is to use the curve to characterize the properties of surfaces where curves lie. Here we focus on the trajectory under the Sasaki magnetic field on real hypersurface of type A;in a complex projective space CP^(n)(c). The Sasaki magnetic field is a closed 2-form defined by the structure of a real hypersurface and the trajectory under the Sasaki magnetic field is the moving loucs of a unit charged particle under the magnetic field. In order to understand the trajectory,it is usually compared with some special simple curves,such as geodesic,circle,etc. In this paper,we analyze the relationship between the extrinsic geodetic curvature and the extrinsic complex torsion of the extrinsic circular trajectories under Sasaki magnetic field on the real hypersurface of type A;in a complex projective space CP^(n)(c).