The Construction Of Equidistant Spheres And Generalized Equidistant Spheres And Basic Domains On Quaternion Hyperbolic Space

In this thesis,we main investigate the fundamental domain in quaternionic hyperbolic space.Let G be a discrete subgroup of PSp(n,1).For a boundary point y of the siegel domain,we define the generalized isometric spheres ly(f)of an element f of PSp(n,1).Using the generalized isometric spheres of elements of G,we construct a fundamental domain Py(G)for G,which is regarded as a generalization of the Ford domain.We also show that the Dirichlet polyhedron D(w)for G with center w converges to Py(G)as w?y.We now outline the layout of this thesis:Firstly,in Chapter one,we will give some back-ground for our main investigation in this thesis.Secondly,in Chapter two,we will provide some background knowledge:the basic knowledge of quaternion,the matrix of quaternion,the quaternionic hyperbolic space and horosphere coordinate.In the end,we will show our main result,in Chapter three to Chapter six.