Conditions For Hypersurfaces With Three Different Principal Curvatures In Spherical Space To Be 2-type Rotational Hypersurfaces

Starting from the 2-type rotational hypersurface in the space form,this thesis first calculates the first and second fundamental forms of the 2-type rotational hypersurface,and then gives the condition that the hypersurface with three different principal curvatures in the spherical space is the 2-type rotational hypersurface.This theorem extends the relevant results of the 1-type rotational hypersurface of M Do Carmo and D M Dajczer to the 2-type rotational hypersurface.In addition to the above results,this thesis also constructs an example of three minimal Willmore hypersurfaces with different principal curvature.