Rotational Surfaces In The Unit Sphere And The Hyperbolic Space

In this paper, we mainly study rotational surfaces in the unit sphere and the hyper-bolic space and discuss three problems.In the first chapter, we introduce the research background of this paper, some basic theories of submanifolds and the definition of rotational surfaces in hyperbolic space H3.In the second chapter, we study the hypersurfaces in Sn+1which have two principle curvatures one of which is of multiplicity1. Using the method of literature [7]. we can express this hypersurfaces.The literature [11] studies surfaces of constant mean curvature in S3. Because the spaces53and H3are similar, we make use of the method of literature [11] in the third chapter to study the rotational surfaces with constant mean curvature in H3and prove that they are embedded.