Abstract
By means of inversion with respect to a sphere in space, torus will be transformed to surface, called cyclide. The parabolic cyclide will be shown in this thesis. Also, the deformation of Dupin cyclide illustrated by a symmetric Dupin horn cyclide will be demonstrated, too. Based on Steiner porism, Steiner annulus 3-chain(sphere case) is studied in this thesis. To obtain the geometric properties similiar to Steiner porism on surface of cyclide, we intend to focus on three mutually tangential spheres in Dupin ring cyclide. keywords: Inversion; Dupin cyclide; Steiner porism.