Study On The Trajectories For Sasakian Magnetic Field On Real Hypersurfaces Of Type A₂ In A Complex Projective Space

It is an important subject in differential geometry to obtain the characterizations of the surface where the curve is located by using the properties of the curve on the surface.In this thesis,the real hypersurface of type A₂ in a complex projective space is taken as the research object,and the Sasakian magnetic field associated with the geometric structure of the real hypersurface is considered.By analyzing the trajectories of the unit charged particle for Sasakian magnetic field,the characterizations of the real hypersurface type A₂ are analyzed.The main work includes the following three aspects.1.The condition that the extrinsic shape of the trajectories for Sasakian magnetic field on real hypersurfaces of type A₂ in a complex projective space becomes a circle is obtained.2.By using the condition that the extrinsic shape of the trajectories for Sasakian magnetic field on real hypersurfaces of type A₂ in a complex projective space becomes a circle,the extrinsic geodesic curvature and the extrinsic complex torsion of the extrinsic circular trajectories for Sasakian magnetic field on real hypersurfaces of type A₂ in a complex projective space are obtained.At the same time,the relationship between the extrinsic geodesic curvature and the extrinsic complex torsion of the extrinsic circular trajectories for Sasakian magnetic field on real hypersurfaces of type A₂ in a complex projective space is analyzed.Then the moduli space of the extrinsic circular trajectories for Sasakian magnetic field on real hypersurfaces of type A₂ in a complex projective space is given.3.Considering the condition that the extrinsic shape of the trajectories for Sasakian magnetic fields on real hypersurfaces of type A₂ in a complex projective space becomes a circle,the geodesic for Sasakian magnetic field on real hypersurfaces of type A₂ in a complex projective space is considered.The situation that the extrinsic shape of the geodesic for Sasakian magnetic field on real hypersurfaces of type A₂ in a complex projective space becomes a circle is discussed.