复双曲空间中测地球面上的Sasakian磁流

Measuring Sasakian Magnetic Flow on Earth Surface in Complex Hyperbolic Space

摘要: 在复双曲空间中的每个测地球上都有由几乎接触度量结构引起的Sasakian磁场。在本文中研究了复双曲空间中测地球上的一种特殊的Sasakian磁流即Legendre轨道流，它是带电粒子在测地球上的Sasakian磁场作用下沿着与特征向量场正交方向运动所获得的受限磁流。本文主要研究了复双曲空间中测地球上的Legendre轨道流与Legendre测地流彼此光滑共轭。

Abstract: In the complex hyperbolic space, there are Sasakian magnetic fields caused by the almost contact metric structure on every measuring earth. In this paper, a special Sasakian magnetic flow, Legendre orbital flow, is studied on the measuring Earth in the complex hyperbolic space. It is the limited magnetic flow obtained by the charged particles moving in the direction orthogonal to the eigenvector field under the Sasakian magnetic field on the measured earth. This paper mainly studies that the Legendre orbital flow and Legendre geodesic flow on Earth in complex hyperbolic space are smooth conjugate to each other.